हल कीजिए - `cot . theta/2 - cot theta = cosec . theta/2`

Explanation

दिया है - `cot . theta/2 - cot theta = cosec . theta/2`
`rArr (cos theta//2)/(sin theta//2) - (cos theta)/(sin theta) = 1/( sin theta//2)`
`rArr (sin theta cos theta //2 -cos theta sin theta //2)/(sin theta sin theta//2) = 1/(sin theta//2)`
`rArr sin theta cos . theta/2 - cos theta sin . theta/2 = sin theta`
`rArr 2 sin . theta /2 cos^(2) .theta/2 - 2 cos^(2). theta/2sin . theta/ 2 = 2 sin . theta/2 cos . theta/2`
`rArr sin theta//2 (2 cos theta//2 -1) = 0`
यदि `sin theta//2 = 0`
तब `theta//2 = n pi rArr theta = 2 n pi`
और यदि `2 cos theta//2 - 1 = 0 rArr cos theta//2 = 1/2`
तब `theta//2 = 2 n pi pm pi/3 rArr theta = 4 n pi pm (2pi)/3`