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

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.

shaalaa.com

Is there an error in this question or solution?

Prove that (cosec A – sin A)(sec A – cos A) sec² A = tan A.

`Prove the following trigonometric identities.

`(sec A - tan A)^2 = (1 - sin A)/(1 + sin A)`

Prove the following trigonometric identities.

`(cos theta - sin theta + 1)/(cos theta + sin theta - 1) = cosec theta + cot theta`

If `(x/a sin theta - y/b cos theta) = 1` and `(x/a cos theta + y/b sin theta) = 1`, prove that `(x^2/a^2 + y^2/b^2) = 2`.

Prove that `(sinθ - cosθ + 1)/(sinθ + cosθ - 1) = 1/(secθ - tanθ)`

Without using trigonometric table , evaluate :

`(sin49^circ/sin41^circ)^2 + (cos41^circ/sin49^circ)^2`

Prove that : `(sin(90° - θ) tan(90° - θ) sec (90° - θ))/(cosec θ. cos θ. cot θ) = 1`

Prove that `( tan A + sec A - 1)/(tan A - sec A + 1) = (1 + sin A)/cos A`.

If cos A + cos²A = 1, then sin²A + sin⁴A = ?

Prove the following:

(sin α + cos α)(tan α + cot α) = sec α + cosec α