Mark the Correct alternative in the following:

If cos 2x + 2 cos x = 1 then, (2 – cos2 x) sin2 x is equal to


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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