Question

Prove the following trigonometric identities.

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

Answer 1

We need to prove `(1 + cos A)/sin^2 A = 1/(1 - cos A)`

Using the property `cos^2 theta + sin^2 theta = 1` we get

LHS = `(1 + cos A)/sin^2 A = (1 + cos A)/(1 - cos^2 A)`

Further using the identity,  `a^2 - b^2 = (a + b)(a - b)` we get

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

`= 1/(1 - cos A)`

= RHS

Hence proved.