Question

3sintheta+4costhetha=5 find the value of 4sin-3cos

Answer 1

3 sin x + 4 cos x = 5

[3 sin x + 4 cos x]² = 25

9 sin²x + 16 cos²x + 24 sin x . cos x = 25

9(1 − cos²x) + 16(1−sin²x) + 24 sin x . cos x = 25

−9 cos²x − 16 sin²x + 25 + 24 sin x . cos x = 25

9 cos²x + 16 sin²x − 24 sin x . cos x = 0

[3 cos x − 4 sin x]² = 0

3 cos x − 4 sin x = 0

4 sin x − 3 cos x = 0 (Ans.)

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