Trigonometric identity: |

Applying [ tan A = sin A / cos A ] to the LHS,

Simplifying the numerator by taking cos

^{2}A as the common denominator,

From the identity [ sin

^{2}θ + cos

^{2}θ = 1 ], it follows that [ sin

^{2}θ = 1 - cos

^{2}θ ],

Add two two cos

^{2}A in the numerator,

Comparing the numerator with a

^{2}+ b

^{2}+ 2ab, a is cos

^{2}A and b is 1. Thus, applying (a + b)

^{2}= a

^{2}+ b

^{2}+ 2ab,

Cancel the common (1 - cos

^{2}A) from the numerator and denominator,

Applying [ sin

^{2}θ = 1 - cos

^{2}θ ],

... which is the RHS expression

Trigonometric identities used:

- tan A = sin A / cos A
- sin
^{2}θ + cos^{2}θ = 1