Question

Solve the equation 4 sin x - cosec x =cot x for 0° < x < 360°. ​

Answer 1

For this question, I will be writing 'csc' instead of 'cosec'

`4\sin x-\csc x=\cot x\\\\4\sin x-(1)/(\sin x)=(\cos x)/(\sin x)\\\\4\sin^(2) x-1=\cos x\\\\4(1-\cos^(2) x)-1=\cos x\\\\4-4\cos^(2) x-1-\cos x=0\\\\4\cos^(2) x+\cos x-3=0\\\\ (4\cos x-3)(\cos x+1)=0\\\\\cos x=(3)/(4), 1\\\\\therefore \boxed{\cos^(-1) \left((3)/(4) \right), 180^(\circ), 360^(\circ)-\cos^(-1) \left((3)/(4) \right)}`