1. What is the value of (cosecA - cotA) / (secA + tanA)?
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By: anil on 05 May 2019 02.13 am
Expression : (cosecA - cotA) / (secA + tanA) Multiplying numerator and denominator by $$(sec A - tan A)$$ = $$frac{cosec A - cot A}{sec A + tan A} imes frac{sec A - tan A}{sec A - tan A}$$ = $$frac{(cosec A - cot A) imes (sec A - tan A)}{sec^2 A - tan^2 A}$$ Now, $$(sec^2 A - tan^2 A) = (cosec^2 A - cot^2 A) = 1$$ = $$frac{(cosec A - cot A) imes (sec A - tan A)}{cosec^2 A - cot^2 A}$$ = $$frac{(cosec A - cot A) imes (sec A - tan A)}{(cosec A - cot A) imes (cosec A + cot A)}$$ = $$frac{sec A - tan A}{cosec A + cot A}$$
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