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Question 170
If 0° ≤ A ≤ 90°, the simplified form of the given expression sin A cos A (tan A - cot A) is
Solution
Expression : $$sin A cos A (tan A - cot A)$$
= $$sin A cos A (\frac{sin A}{cos A} - \frac{cos A}{sin A})$$
= $$sin A cos A (\frac{sin^2 A - cos^2 A}{sin A cos A})$$
= $$sin^2 A - cos^2 A$$
= $$sin^2 A - (1 - sin^2 A)$$
= $$2sin^2 A - 1$$
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