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Question
Prove that `(sin 70°)/(cos 20°) + (cosec 20°)/(sec 70°) - 2 cos 70° xx cosec 20°` = 0.
Solution
LHS = `(sin 70°)/(cos 20°) + (cosec 20°)/(sec 70°) - 2 cos 70° xx cosec 20°`
= `sin (90° - 20°)/(cos 20°) + (cosec(90° - 20°))/(sec 70°) - 2 cos 70° xx cosec 20°`
= `(cos 20°)/(cos 20°) + (sec 70°)/(sec 70°) - 2 cos 70° xx cosec 20°`
= 1 + 1 - 2cos (90° - 20°) . cosec 20°
= 2 - 2 sin 20°. `1/sin 20°`
= 2 - 2
= 0
= RHS
Hence proved.
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