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Question

Solve 1+cosx=sin2x


A
(2n+1)π2 nN
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B

2nπ nN

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C

(2n+1)π nN

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D

nπ nN

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Solution

The correct options are
A (2n+1)π2 nN
C

(2n+1)π nN


Here, we will write sin2x=1cos2x, because there is a 1+cosx on L.H.S. and it will be a common factor.

1+cosx=1cos2x

1+cosx=(1cosx)(1+cosx)

1+cosx=0 or 1cosx=1

cosx=1 or cosx=0
x=π or x=π2

We know that the general solution forumla for the equation
cosx=cosα
is x=2nπ±α
x=(2n±1)π
or x=(2n±1)π2


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