We have to prove the identity
=========> Equation 1
We know
Substituting these in the left hand side in equation 1, we get
Taking the lowest common denominator on both sides, we get
.
This is the left hand side written in terms of sine and cosine.
Also, we know that
Applying this in the left hand side, we get
, which is the simplified form of the left hand side.
Striking off from the numerator and denominator, we get
, which is the left hand side written in terms of
The reciprocal identity states that
Or,
Hence, we use reciprocal identity to simplify the expression into the right hand side.
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