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))#