Question

cosec tita +cot tita=k then prove that cos titA =k2-1/k2+1

Answer 1

Answer:

`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