Prove that (Sin 70°)/(Cos 20°) + (Cosec 20°)/(Sec 70°) - 2 Cos 70° Xx Cosec 20° = 0 - Mathematics

Prove that `(sin 70°)/(cos 20°) + (cosec 20°)/(sec 70°) - 2 cos 70° xx cosec 20°` = 0.

Sum

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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