What is $sintheta-tantheta+cottheta$ in terms of $costheta$ ?

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Answer 1 · 2018-04-08T17:16:39

Please see the explanation below.

We need

$sin^2theta+cos^2theta=1$

$tantheta=sintheta/costheta$

$cottheta=costheta/sintheta$

Therefore,

$sintheta-tantheta+cottheta$

$=sintheta-sintheta/costheta+costheta/sintheta$

$=sqrt(1-cos^2theta)-sqrt(1-cos^2theta)/costheta+costheta/sqrt(1-cos^2theta)$

$=(costheta(1-cos^2theta)-(1-cos^2theta)+cos^2theta)/(costhetasqrt(1-cos^2theta))$

$=(costheta-cos^3theta-1+cos^2theta+cos^2theta)/(costhetasqrt(1-cos^2theta))$

$=(costheta+2cos^2theta-cos^3theta-1)/(costhetasqrt(1-cos^2theta))$

What is sintheta-tantheta+cotthetasintheta-tantheta+cottheta in terms of costhetacostheta?