Q. 4

# Mark the Correct alternative in the following:If cos 2x + 2 cos x = 1 then, (2 – cos2 x) sin2 x is equal toA.1B. -1C. D.

Given cos 2x + 2 cos x = 1, we need to find the expression,

(2 – cos2 x) sin2 x

Consider cos 2x + 2 cos x = 1

2cos2 x – 1 + 2 cos x -1 = 0

2cos2 x + 2cos x – 2 = 0

cos2 x + cos x = 1 -------- (1)

Now consider the expression

(2 – cos2 x) sin2 x = (2 – cos2 x)(1-cos2x)

= {2 – (1 – cos x)} { 1- ( 1 – cos x)}

[from equation (1) cos2 x = 1 - cos x]

= (1+ cos x) ( cos x)

= cos x + cos2 x

[from equation (1) cos2 x + cos x = 1]

= 1

Hence (2 – cos2 x) sin2 x = 1, so option A is the answer.

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