Question

If `cosec theta + cot theta =k` then prove that `cos theta = (k^2-1)/(k^2+1)`

Answer 1

`1/(sin theta) + cos theta/sin theta = k`
`1 + cos theta= k sin theta`
`(1 + cos theta)^2 = k^2 sin^2 theta`
`(1 + cos theta)^2 = k^2( 1- cos^2 theta)`
`( 1 + cos theta)^2 = k^2 (1 + cos theta)(1 - cos theta)`
`( 1 + cos theta) = k^2 - k^2 cos theta`
`k^2 cos theta + cos theta = k^2 - 1`
`cos theta ( k^2 + 1) = k^2 - 1`
`cos theta = (k^2 - 1)/(k^2 + 1)`
option 2 is correct
Answer