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Question

Square relations among various trigonometrical ratios
sin2θ+cos2θ=1
sec2θtan2=1
cosec2θcot2θ=1
These are also called Pythagorean identities.

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Solution

LetΔABCABC=90sin2θ+cos2θ=1sec2θtan2=1cosec2θcot2θ=1Sinθ=ph,cosθ=bhbyusingpythagorastheoramP2+b2=h2p2h2+b2h2=1sin2θ+cos2θ=1(proved)sec2θtan2=1h2b2+p2b2=1h2+p2b2=1b2b2=1(proved)andcosec2θcot2θ=1h2p2b2p2=1h2b2p2=1p2p2=1(proved)


1181450_1214883_ans_eb556ed01d8140289a6f0bcee15ba1fe.jpg

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