Question

2sinA + 3cosA = 2

Prove that:

3sinA - 2cosA = +/- 3

Answer 1

Question #54707– Math – Trigonometry

2 sin A + 3 cos A = 2

Prove that:

3 sin A - 2 cos A = ± 3

Proof:

2 sin A + 3 cos A = 2

Squaring both sides:

4 sin² A + 12 sin A cos A + 9 cos² A = 4

Using the identity:

sin² A + cos² A = 1

4(1 - cos² A) + 12 sin A cos A + 9(1 - sin² A) = 4

Expanding:

4 - 4 cos² A + 12 sin A cos A + 9 - 9 sin² A = 4

4 cos² A - 12 sin A cos A + 9 sin² A = 9

(3 sin A - 2 cos A)² = 9

So

3 sin A - 2 cos A = ± 3

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