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3sinx+4cosx=5 then what is the value of 4sinx-3cosx

3sinx+4cosx=5 then what is the value of  4sinx-3cosx

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1 Answers

Vikas TU
14149 Points
4 years ago
Dear student
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
Good Luck 

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