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Question
Prove that sec2θ + cosec2θ = sec2θ × cosec2θ
Solution
L.H.S = sec2θ + cosec2θ
= `1/(cos^2theta) + 1/(sin^2theta)`
= `(sin^2theta + cos^2theta)/(cos^2theta*sin^2theta)`
= `1/(cos^2theta*sin^2theta)` ......[∵ sin2θ + cos2θ = 1]
= `1/(cos^2theta) xx 1/(sin^2theta)`
= sec2θ × cosec2θ
= R.H.S
∴ sec2θ + cosec2θ = sec2θ × cosec2θ
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