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Some Applications Of Trigonometry

Question

Prove the following identities where the angles involved are acute angles for which the expressions are defined.
$fraction numerator tanθ over denominator 1 minus cotθ end fraction plus fraction numerator cotθ over denominator 1 minus tanθ end fraction space equals space 1 plus secθ. space cosecθ$

Solution

fraction numerator tanθ over denominator 1 minus cotθ end fraction plus fraction numerator cotθ over denominator 1 minus tanθ end fraction space equals space 1 plus secθ. space cosecθ

Hence, L.H.S. = R.H.S.