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Question
Prove that:
sec2θ + cosec2θ = sec2θ x cosec2θ
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Solution
L.H.S = sec2θ + cosec2θ
= 1 + tan2θ + 1 + cot2θ .....[∵ sec2θ = 1 + tan2θ and cosec2θ = 1 + cot2θ]
= 2 + tan2θ + cot2θ .....(i)
R.H.S = sec2θ x cosec2θ
= (1 + tan2θ) x (1 + cot2θ) .....[∵ sec2θ = 1 + tan2θ and cosec2θ = 1 + cot2θ]
= 1 + cot2θ + tan2θ + tan2θ x cot2θ
= 1 + cot2θ + tan2θ + tan2θ x (1/tan2θ) ...... [∵ cot2θ = 1/tan2θ]
= 2 + tan2θ + cot2θ .......(ii)
From (i) and (ii)
sec2θ + cosec2θ = sec2θ x cosec2θ
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