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Question

Given f(x)=tanx. Then f(x) is equal to


A

sec2x

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B

cosec2x

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C

sec2x

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D

xsec2x

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Solution

The correct option is A

sec2x


f(x)=tanx

We can write
tanx as sinxcosx

f(x)=sinxcosx=g(x)h(x)

We know,
f(x)=h(x)g(x)h(x)g(x)(h(x))2
=cosxsin(x)cos(x)sinx(cosx)2

=cosxcosx(sinx)(sinx)(cosx)2
=cos2x+sin2xcos2x
=sec2
f(x)=sec2x x (π2,π2)


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