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Question

If x = cosec A + cos A and y = cosec A - cos A then prove that

(2x+y)2+(xy2)21=0

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Solution

X = cosec A + cos A y = cosec A - cos A
=> x+y = 2 cosec A
=> 2/(x+y) = sinA

(x - y)/2 = cos A

LHS = [ 2/(x+y) ]² + [(x-y)/2]² - 1
= sin² A + cos ² A - 1
= 1 - 1 = 0


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