Question

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Answer 1

This Picture Answer

Step-by-step explanation:

The given equation can be written as

2sin(x/2)(cos2x−sin2x)=cos2x−sin2x

⇒(2sin(x/2)−1)cos2x=0

Hence cos2x=0 or sin(x/2)=1/2

i.e. 2x=nπ+π/2 or

x/2=kπ+(−1)k(π/6)(n,kεI). 

In other words,

x=nπ/2+π/4 or x=2kπ+(−1)kπ/3

If x=nπ/2+π/4, then sin2x=±1, 

and if  x=2kπ+(−1)kπ/3,cosx

=cos(π/3)=1/2 

and cos2x=cos(2π/3)=−1/2.

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