Question

Sin A = tanA\√1 + tan^2A?

Answer 1

See below for whole explanation.

Explanation:

`tan A = sin A/cos A`

Substitute `cos A` with `sqrt(1-sin^2 A)`.

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

Square both sides.

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

Multiply both sides by `1-sin^2 A`.

`tan^2 A - sin^2 A tan^2 A = sin^2 A`

Add `sin^2 A * tan^2 A` to both sides and take `sin^2 A` common factor on the right side.

`tan^2 A = sin^2 A (1 + tan^2 A)`

Divide by 1+tan^2 A on both side, and :

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

Finally, take the square root of both sides.

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