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

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

Sum

LHS = `( tan A + sec A - 1)/(tan A - sec A + 1)`

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

= `(( tan A + sec A)( 1 - sec A + tan A))/(tan A - sec A + 1)`

= tan A + sec A

= `sin A/cos A + 1/cos A = (1 + sin A)/cos A`

= RHS

Hence proved.

shaalaa.com

Is there an error in this question or solution?

If sinθ + sin² θ = 1, prove that cos² θ + cos⁴ θ = 1

Show that `sqrt((1-cos A)/(1 + cos A)) = sinA/(1 + cosA)`

Prove the following trigonometric identities.

`(cot A + tan B)/(cot B + tan A) = cot A tan B`

`(cos^3 θ + sin^3 θ)/(cos θ + sin θ) + (cos ^3 θ - sin^3 θ)/(cos θ - sin θ) = 2`

Simplify : 2 sin30 + 3 tan45.

cos⁴ A − sin⁴ A is equal to ______.

Without using trigonometric identity , show that :

`sec70^circ sin20^circ - cos20^circ cosec70^circ = 0`

Prove the following identities.

cot θ + tan θ = sec θ cosec θ

Show that: `tan "A"/(1 + tan^2 "A")^2 + cot "A"/(1 + cot^2 "A")^2 = sin"A" xx cos"A"`

(sec² θ – 1) (cosec² θ – 1) is equal to ______.