How to use the trigonometric identity $cos(2A)=1-2sin^2(A)$ to show that $sinleft(fracpi12right)=sqrtfrac12 - fracsqrt34$ [closed]

Clash Royale CLAN TAG#URR8PPP

up vote
0
down vote

favorite

Question: Use the trigonometric identity $cos(2A)=1-2sin^2(A)$ to show that $$sinleft(fracpi12right)=sqrtfrac12 - fracsqrt34$$

What are good strategies to figure out this question in Particular?

trigonometry

share|cite|improve this question

edited Aug 6 at 4:28

Abhas Kumar Sinha

10011

asked Jul 30 at 8:21

laquishabonquiquithe3rd

11

closed as off-topic by Delta-u, amWhy, Rhys Steele, Mostafa Ayaz, Isaac Browne Jul 30 at 19:46

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Delta-u, amWhy, Rhys Steele, Mostafa Ayaz, Isaac Browne

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Make $2A=frac pi 6$ to compute $sin^2(A)$ and then ???
  – Claude Leibovici
  Jul 30 at 8:25
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Welcome to MathSE. Please read this tutorial on how to typeset mathematics on this site.
  – N. F. Taussig
  Jul 30 at 9:50
  

  
  
  
  

add a comment | 

up vote
0
down vote

favorite

Question: Use the trigonometric identity $cos(2A)=1-2sin^2(A)$ to show that $$sinleft(fracpi12right)=sqrtfrac12 - fracsqrt34$$

What are good strategies to figure out this question in Particular?

trigonometry

share|cite|improve this question

edited Aug 6 at 4:28

Abhas Kumar Sinha

10011

asked Jul 30 at 8:21

laquishabonquiquithe3rd

11

closed as off-topic by Delta-u, amWhy, Rhys Steele, Mostafa Ayaz, Isaac Browne Jul 30 at 19:46

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Delta-u, amWhy, Rhys Steele, Mostafa Ayaz, Isaac Browne

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Make $2A=frac pi 6$ to compute $sin^2(A)$ and then ???
  – Claude Leibovici
  Jul 30 at 8:25
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Welcome to MathSE. Please read this tutorial on how to typeset mathematics on this site.
  – N. F. Taussig
  Jul 30 at 9:50
  

  
  
  
  

add a comment | 

up vote
0
down vote

favorite

up vote
0
down vote

favorite

Question: Use the trigonometric identity $cos(2A)=1-2sin^2(A)$ to show that $$sinleft(fracpi12right)=sqrtfrac12 - fracsqrt34$$

What are good strategies to figure out this question in Particular?

trigonometry

share|cite|improve this question

edited Aug 6 at 4:28

Abhas Kumar Sinha

10011

asked Jul 30 at 8:21

laquishabonquiquithe3rd

11

Question: Use the trigonometric identity $cos(2A)=1-2sin^2(A)$ to show that $$sinleft(fracpi12right)=sqrtfrac12 - fracsqrt34$$

What are good strategies to figure out this question in Particular?

trigonometry

share|cite|improve this question

edited Aug 6 at 4:28

Abhas Kumar Sinha

10011

asked Jul 30 at 8:21

laquishabonquiquithe3rd

11

share|cite|improve this question

share|cite|improve this question

edited Aug 6 at 4:28

Abhas Kumar Sinha

10011

edited Aug 6 at 4:28

Abhas Kumar Sinha

10011

edited Aug 6 at 4:28

Abhas Kumar Sinha

10011

10011

asked Jul 30 at 8:21

laquishabonquiquithe3rd

11

asked Jul 30 at 8:21

laquishabonquiquithe3rd

11

asked Jul 30 at 8:21

laquishabonquiquithe3rd

11

11

closed as off-topic by Delta-u, amWhy, Rhys Steele, Mostafa Ayaz, Isaac Browne Jul 30 at 19:46

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Delta-u, amWhy, Rhys Steele, Mostafa Ayaz, Isaac Browne

If this question can be reworded to fit the rules in the help center, please edit the question.

closed as off-topic by Delta-u, amWhy, Rhys Steele, Mostafa Ayaz, Isaac Browne Jul 30 at 19:46

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Delta-u, amWhy, Rhys Steele, Mostafa Ayaz, Isaac Browne

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Make $2A=frac pi 6$ to compute $sin^2(A)$ and then ???
  – Claude Leibovici
  Jul 30 at 8:25
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Welcome to MathSE. Please read this tutorial on how to typeset mathematics on this site.
  – N. F. Taussig
  Jul 30 at 9:50
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Make $2A=frac pi 6$ to compute $sin^2(A)$ and then ???
  – Claude Leibovici
  Jul 30 at 8:25
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Welcome to MathSE. Please read this tutorial on how to typeset mathematics on this site.
  – N. F. Taussig
  Jul 30 at 9:50
  

  
  
  
  

1

1

Make $2A=frac pi 6$ to compute $sin^2(A)$ and then ???
– Claude Leibovici
Jul 30 at 8:25

Make $2A=frac pi 6$ to compute $sin^2(A)$ and then ???
– Claude Leibovici
Jul 30 at 8:25

Welcome to MathSE. Please read this tutorial on how to typeset mathematics on this site.
– N. F. Taussig
Jul 30 at 9:50

Welcome to MathSE. Please read this tutorial on how to typeset mathematics on this site.
– N. F. Taussig
Jul 30 at 9:50

add a comment | 

2 Answers
2

active

oldest

votes

up vote
1
down vote

Use the trigonemetric identity, we get $sinA=pmsqrtfrac1-cos2A2$

Substitute $A=fracpi12$ in it, we can easily find that $sin A>0$. Therefore $sinfracpi12=sqrtfrac1-cosfracpi62=sqrtfrac1-fracsqrt322=sqrtfrac12-fracsqrt34$

share|cite|improve this answer

answered Jul 30 at 8:57

LJFan

112

add a comment | 

up vote
0
down vote

$$cos(2A)=1-2sin^2(A)$$

$$cos(pi /6)=1-2sin^2(pi /12)$$

$$1-2sin^2(pi /12)=frac sqrt 32$$

$$2sin^2(pi /12)=1-frac sqrt 32$$
$$
sin^2(pi /12)=frac 12-frac sqrt 34$$
$$sin(pi /12)=sqrt frac 12-frac sqrt 34$$

share|cite|improve this answer

answered Jul 30 at 10:04

Mohammad Riazi-Kermani

27.3k41851

add a comment | 

2 Answers
2

active

oldest

votes

2 Answers
2

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
1
down vote

Use the trigonemetric identity, we get $sinA=pmsqrtfrac1-cos2A2$

Substitute $A=fracpi12$ in it, we can easily find that $sin A>0$. Therefore $sinfracpi12=sqrtfrac1-cosfracpi62=sqrtfrac1-fracsqrt322=sqrtfrac12-fracsqrt34$

share|cite|improve this answer

answered Jul 30 at 8:57

LJFan

112

add a comment | 

up vote
1
down vote

Use the trigonemetric identity, we get $sinA=pmsqrtfrac1-cos2A2$

Substitute $A=fracpi12$ in it, we can easily find that $sin A>0$. Therefore $sinfracpi12=sqrtfrac1-cosfracpi62=sqrtfrac1-fracsqrt322=sqrtfrac12-fracsqrt34$

share|cite|improve this answer

answered Jul 30 at 8:57

LJFan

112

add a comment | 

up vote
1
down vote

up vote
1
down vote

Use the trigonemetric identity, we get $sinA=pmsqrtfrac1-cos2A2$

Substitute $A=fracpi12$ in it, we can easily find that $sin A>0$. Therefore $sinfracpi12=sqrtfrac1-cosfracpi62=sqrtfrac1-fracsqrt322=sqrtfrac12-fracsqrt34$

share|cite|improve this answer

answered Jul 30 at 8:57

LJFan

112

Use the trigonemetric identity, we get $sinA=pmsqrtfrac1-cos2A2$

Substitute $A=fracpi12$ in it, we can easily find that $sin A>0$. Therefore $sinfracpi12=sqrtfrac1-cosfracpi62=sqrtfrac1-fracsqrt322=sqrtfrac12-fracsqrt34$

share|cite|improve this answer

answered Jul 30 at 8:57

LJFan

112

share|cite|improve this answer

share|cite|improve this answer

answered Jul 30 at 8:57

LJFan

112

answered Jul 30 at 8:57

LJFan

112

answered Jul 30 at 8:57

LJFan

112

112

add a comment | 

add a comment | 

up vote
0
down vote

$$cos(2A)=1-2sin^2(A)$$

$$cos(pi /6)=1-2sin^2(pi /12)$$

$$1-2sin^2(pi /12)=frac sqrt 32$$

$$2sin^2(pi /12)=1-frac sqrt 32$$
$$
sin^2(pi /12)=frac 12-frac sqrt 34$$
$$sin(pi /12)=sqrt frac 12-frac sqrt 34$$

share|cite|improve this answer

answered Jul 30 at 10:04

Mohammad Riazi-Kermani

27.3k41851

add a comment | 

up vote
0
down vote

$$cos(2A)=1-2sin^2(A)$$

$$cos(pi /6)=1-2sin^2(pi /12)$$

$$1-2sin^2(pi /12)=frac sqrt 32$$

$$2sin^2(pi /12)=1-frac sqrt 32$$
$$
sin^2(pi /12)=frac 12-frac sqrt 34$$
$$sin(pi /12)=sqrt frac 12-frac sqrt 34$$

share|cite|improve this answer

answered Jul 30 at 10:04

Mohammad Riazi-Kermani

27.3k41851

add a comment | 

up vote
0
down vote

up vote
0
down vote

$$cos(2A)=1-2sin^2(A)$$

$$cos(pi /6)=1-2sin^2(pi /12)$$

$$1-2sin^2(pi /12)=frac sqrt 32$$

$$2sin^2(pi /12)=1-frac sqrt 32$$
$$
sin^2(pi /12)=frac 12-frac sqrt 34$$
$$sin(pi /12)=sqrt frac 12-frac sqrt 34$$

share|cite|improve this answer

answered Jul 30 at 10:04

Mohammad Riazi-Kermani

27.3k41851

$$cos(2A)=1-2sin^2(A)$$

$$cos(pi /6)=1-2sin^2(pi /12)$$

$$1-2sin^2(pi /12)=frac sqrt 32$$

$$2sin^2(pi /12)=1-frac sqrt 32$$
$$
sin^2(pi /12)=frac 12-frac sqrt 34$$
$$sin(pi /12)=sqrt frac 12-frac sqrt 34$$

share|cite|improve this answer

answered Jul 30 at 10:04

Mohammad Riazi-Kermani

27.3k41851

share|cite|improve this answer

share|cite|improve this answer

answered Jul 30 at 10:04

Mohammad Riazi-Kermani

27.3k41851

answered Jul 30 at 10:04

Mohammad Riazi-Kermani

27.3k41851

answered Jul 30 at 10:04

Mohammad Riazi-Kermani

27.3k41851

27.3k41851

add a comment | 

add a comment |