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Question

1+cos thita - sin thita/ cos thita -1+ sin thita = cosec thita + cot thita

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Solution

LHS =

cosθ-sinθ+1 /cos θ + sinθ-1

Divide numerator and denominator by sinθ

=> cosecθ + Cotθ - 1 / cotθ - Cosecθ + 1

=> cosecθ + Cotθ - ( cosecθ^2 - Cotθ^2) / cotθ - Cosecθ + 1

=>cosecθ+ Cotθ - (cosecθ + Cotθ) (cosecθ - Cotθ) /cotθ - Cosecθ + 1

=>(cosecθ + Cotθ)( cotθ - Cosecθ + 1 ) / cotθ - cosecθ +1

=>cosecθ + Cotθ


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