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3sinx+4cosx=5 then what is the value of 4sinx-3cosx
Dear student3 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 = 0Good Luck
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