Question

Prove that : 1+cos a/ 1-cos a = tan^(2) a/(sec a - 1)^(2)

Answer 1

To prove (1+cos A)/(1−cos A)=(tan² A)/(sec A−1)²
RHS=(tan² A)/(sec A−1)²=(sec²A−1)/(sec A−1)² ......since sec²A=1+tan²A
={(secA−1)(secA+1)}/(sec A−1)²
={(secA+1)}/(sec A−1)......cancelling (sec A−1) in numerator and denominator
=(1/cosA+1)}/(1/cos A−1)
={(1+cosA)/cosA}/(1−cosA)/cosA}
={(1+cosA)/cosA}/{(1−cosA)/cosA}.
=(1+cosA)/(1−cosA )........cancelling cosA in numerator and denominator
=LHS
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