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Question
prove that `1/(1 + cos(90^circ - A)) + 1/(1 - cos(90^circ - A)) = 2cosec^2(90^circ - A)`
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Solution
LHS = `1/(1 + cos(90^circ - A)) + 1/(1 - cos(90^circ - A))`
= `1/(1 + sinA) + 1/(1 - sinA)`
= `(1 - sinA + 1 + sinA)/((1 + sinA)(1 - sinA))`
= `2/(1 - sin^2A)`
= `2/cos^2A`
= `2sec^2A = 2cosec^2(90^circ - A)`
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