Question

Solve `cot(x//2)-cosec (x//2)=cot x`.

Answer 1

Correct Answer - `x=4 n pi pm (2pi)/3, n in Z`
`(cos (x//2))/(sin (x//2)) - (cos x)/(2 sin (x//2) cos (x//2)) = (1)/(sin (x//2))`
`rArr 2 cos^(2) (x//2) - cos(x) = 2 cos(x//2)`
`rArr 1 + cos x - cos x = 2 cos (x//2)`
`rArr cos (x//2) = 1//2 = cos (pi//3)`
`rArr x//2 = 2n pi -+pi//3, n in Z`
`rArr x = 4n pi -+ 2 pi//3, n in Z`