Search This Blog

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: