Trigonometric identities - 14

Trigonometric identity:

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

Simplifying the numerator by taking cos² A as the common denominator,

Applying (a/b)/c = a/(bc),

From the identity [ sin²θ + cos²θ = 1 ], it follows that [ sin²θ = 1 - cos²θ ],

Add two two cos²A in the numerator,

Comparing the numerator with a² + b² + 2ab, a is cos²A and b is 1. Thus, applying (a + b)² = a² + b² + 2ab,

Cancel the common (1 - cos²A) from the numerator and denominator,

Applying [ sin²θ = 1 - cos²θ ],

 ... which is the RHS expression

Trigonometric identities used:

•  tan A = sin A / cos A 
•  sin²θ + cos²θ = 1