We know that sin2x + cos2x = 1We know that sin2x = 2sinxcosxDivide numerator and denominator by cos22xWe know that 1 + tan2x = sec2xSubstitute tan2x = tDifferentiate with respect to x⇒ dt = 2sec22xdxHenceResubstitute tHence

Q. 255.0( 3 Votes )

Evaluate: <span l

Class 12th Mathematics - Board Papers All India - 2014

Answer :

We know that sin²x + cos²x = 1

We know that sin2x = 2sinxcosx

Divide numerator and denominator by cos²2x

We know that 1 + tan²x = sec²x

Substitute tan2x = t

Differentiate with respect to x

⇒ dt = 2sec²2xdx

Hence

Resubstitute t

Hence

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