If `2 tan^(-1)(costheta) = tan^(-1)(2 cosec theta)`, then show that `theta = (pi)/(4)`, when n is an y integer.

Answer

N/a

Explanation

We have, `2 cos tan^(-1)(costheta)=tan^(-1)(2 cosec theta)`
`rArr tan^(-1)'((2 costheta)/(1-costheta))=tan^(-1)(2cosestheta)`
`[:'2tan^(-1)x=tan^(-1)((2x)/(1-x^(2)))]`
`rArr ((2costheta)/(sin^(2)theta))=(2cosectheta)`
`rArr (cottheta.2cosectheta) = (2cosectheta)rArr cot theta = 1`
`rArr cot theta = cot(pi)/(4) rArr theta = (pi)/(4)`