Question

prove that 2sin
$\frac{\pi}{8}$
=
$\frac{\pi}{8} \sqrt{2 - \sqrt{2} }$
​

Answer 1

Answer:

We have,

sinx

3

−1

+

cosx

3

+1

=4

2

⇒

sinxcosx

(

3

−1)cosx+(

3

+1)sinx

=4

2

(

3

−1)cosx+(

3

+1)sinx=2

2

sin2x

2

2

3

−1

cosx+

2

2

3

+1

sinx=sin2x

sin(x+

12

5π

)=sin2x

General solution is

x+

12

5π

=nπ+(−1)

n

2x

For n=0,x=

12

5π

For n=1,3x=

12

7π

⇒x=

36

7π

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