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Question

ddx( sec2 x + cosec2 x)=


A

4 cosec 2x cot 2x

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B

-4 cosec 2x cot 2x

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C

4 cosec x cot 2x

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D

None of these

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Solution

The correct option is B

-4 cosec 2x cot 2x


Finding the value of fraction numerator d over denominator d x end fraction square root of left parenthesis space s e c squared space x space plus space cos e c squared space x right parenthesis end root equals

Given, y = ( sec2 x + cosec2 x)

= 1cos2x + 1sin2 x = sin2 x +cos2 xcos2 x sin2 x = 1cos x sin x = 2sin 2x = 2 cosec 2x

Differentiate it with respect to x, we get

dydx = 2 ×-cosec 2x cot 2x ×2 = -4 cosec 2x cot 2x

Hence, option (B) is correct.


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