हल कीजिए : ` cot. (theta)/2 - cot theta = "cosec" (theta)/2.`

Explanation

` cot theta/2 - cot theta = "cosec" theta/2 `
` (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/2 sintheta)= 1/(sin. theta/2)`
` rArr sin ( theta - theta/2) = sin theta `
` rArr sin. theta/2 = 2 sin theta /2 cos. theta/2 `
` rArr sin . theta/2 = 0 " या " 1- 2 cos. theta/2 = 0 `
अब ` sin. theta/2 =0`
`rArr theta/2 = n pi`
`rArr theta = 2n pi `
और ` 1- 2 cos . theta/2 = 0 `
` rArr 2 cos. theta/2 = 1`
` rArr cos. theta /2 = 1/2 = cos . pi/2 `
` rArr theta/2 = 2npi pm pi/3 `
` rArr theta = 4 n pi pm (2pi)/3 `