Question

If tan A = √3 sin A, then find the value of cos² A - sin² A
1. \(-1\over3\)
2. \(1\over3\)
3. \(-2\over3\)
4. \(2\over3\)

Answer 1

Correct Answer - Option 1 : \(-1\over3\)

Calculation:

Given tan A = √3 sin A

\(\rm \sin A\over\cos A\) = √3 sin A

cos A = \(1\over\sqrt3\)

cos² A = \(1\over3\)

∵ cos² A + sin² A = 1

1 - sin² A = \(1\over3\)

1 - \(1\over3\) = sin² A

sin² A = \(2\over3\)

Now cos2 A - sin2 A = \(1\over3\) - \(2\over3\)

cos2 A - sin2 A = \(-1\over3\)