Prove that ((Tan 20°)/(Cosec 70°))^2 + ((Cot 20°)/(Sec 70°))^2 = 1

Prove that `((tan 20°)/(cosec 70°))^2 + ((cot 20°)/(sec 70°))^2 = 1`

Sum

LHS = `((tan 20°)/(cosec 70°))^2 + ((cot 20°)/(sec 70°))^2`

= `((sin 20°. sin 70°)/(cos 20°))^2 + ((cos 20°. cos 20°)/(sin 20°))^2`

= `[(sin 20°.sin (90° - 20°))/(cos 20°)]^2 + [(cos 20°. cos(90° - 20°))/(sin 20°)]^2`

= `[ (sin 20°.cos 20°)/(cos 20°)]^2 + [(cos 20°. sin 20°)/(sin 20°)]^2`

= sin²20° + cos²20°
= 1
= RHS

Hence proved.

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