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If y = cos2 x2, find 

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NIMCET 2017 Official Paper
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  1. 4x2 sin x2 cos x2
  2. -4x cos x2 sin x2
  3. 2x sin x2 cos x2
  4. -2x cos x2 sin x2

Answer (Detailed Solution Below)

Option 2 : -4x cos x2 sin x2
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Detailed Solution

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Concept:

cos2x = 2cos2x - 1

sin2x = 2sin x cos x

 

Calculation:

Here, y = cos2 x2

Let, x2 = t 

Differentiating with respect to x, we get

⇒2xdx = dt 

⇒ dt/dx = 2x ....(1)

y = cos2t

=

= - sin2x2 × 2x

= -4x cos x2 sin x2

Hence, option (2) is correct. 

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