Consider the LHS of this identity. It can not be simplified directly by applying any of the basic trigonometric identities. Some algebra must be applied first on it so that it can be simplified to the RHS. Multiplying the LHS expression with the conjugate of the denominator:
The denominator can be simplified by applying the identity (a + b)(a - b) = a
2 - b
2,
From the identity sin
2θ + cos
2θ = 1, it follows that cos
2θ = 1 - sin
2θ,
Square roots and powers of 2 cancel each other out,
Distributing the denominator in the numerator,
Applying [ 1 / cos θ = sec θ ] and [ sin θ / cos θ = tan θ ],
sec θ + tan θ
... which is the right hand side expression
Trigonometric identities applied:
