Trigonometric identity: |
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Applying the identities [ tan θ = sin θ / cos θ ] and [ cot θ = cos θ / sin θ ] to the LHS,
Simplifying each rational expression,
Writing sin A - cos A = - (cos A - sin A),
The denominator of both the fractions above is same, cos A - sin A. Adding the two fractions,
Applying the formula a2 - b2 = (a + b)(a - b),
Canceling the common factor (cos A - sin A) from the numerator and denominator,
= cos A + sin A... which is the RHS expression
Trigonometric identities applied:
- tan θ = sin θ / cos θ
- cot θ = cos θ / sin θ