Suppose α,βandthη are angles satisfying 0<α<θ<β<2π˙ Then prove that cosβ−cosαsinα−sinβ=−cotθ

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Question

Suppose $α, β a n d t h η$ are angles satisfying $0 < α < θ < β < \frac{π}{2} ˙$ Then prove that $\frac{sin α - sin β}{cos β - cos α} = - cot θ$

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Suppose

α, β a n d t h η

are angles satisfying

0 < α < θ < β < \frac{π}{2} ˙

Then prove that

\frac{sin α - sin β}{cos β - cos α} = - cot θ

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Question Text

Suppose

α, β a n d t h η

are angles satisfying

0 < α < θ < β < \frac{π}{2} ˙

Then prove that

\frac{sin α - sin β}{cos β - cos α} = - cot θ