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Question
Prove that `(cot(180^circ + theta) sin(90^circ - theta) cos(- theta))/(sin(270^circ + theta) tan(- theta) "cosec"(360^circ + theta))` = cos2θ cotθ
Solution
`(cot(180^circ + theta) sin(90^circ - theta) * cos(- theta))/(sin(270^circ + theta) tan(- theta) "cosec"(360^circ + theta))`
= `(cot theta* costheta costheta)/(- cos theta xx - tantheta xx "cosec" theta)`
= `(cot theta * cos^2theta)/(cos theta tan theta "cosec" theta)`
= `(cot theta * cos^2theta)/(cos theta * sintheta/costheta * 1/sin theta)`
= `cos^2theta * cottheta`
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