If cosecA - cot A = q then prove that (q²-1/q²+1)+ cos A =0
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Step-by-step explanation:
There is a mistake in the question. It should be (q²-1)/(q²+1) -1/cos A = 0
Cosec A - cot A = q
1/q = 1/(cosec A - cot A)
= (cosecA + cotA) / [(cosec A + cotA) (cosec A - cot A)
= (cosec A + cot A )/ 1
q + 1/q = (q²+1) / q = 2 cosec A -- (1)
q - 1/q = (q² - 1) / q = - 2 cot A -- (2)
(2) ÷ (1) =>
(q² -1) / (q² + 1) = - cosec A / cot A
= - sec A
LHS = (q² - 1) / (q² + 1) + 1/cos A
= -sec A + sec A
= 0
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