Question

If sec thetha +cos theta =p then find cosec theta

Answer 1

HI MATE.......

secθ+tanθ=p ----------------------(1)

∵, sec²θ-tan²θ=1

or, (secθ+tanθ)(secθ-tanθ)=1

or, secθ-tanθ=1/p ----------------(2)

Adding (1) and (2) we get,

2secθ=p+1/p

or secθ=(p²+1)/2p

∴ cosθ=1/secθ=2p/(p²+1)

∴ sinθ=√(1-cos²θ)

=√[1-{2p/(p²+1)}²]

=√[1-4p²/(p²+1)²]

=√[{(p²+1)²-4p²}/(p²+1)²]

=√[(p⁴+2p²+1-4p²)/(p²+1)²]

=√(p⁴-2p²+1)/(p²+1)

=√(p²-1)²/(p²+1)

=(p²-1)/(p²+1)

∴ cosecθ=1/sinθ=1/[(p²-1)/(p²+1)]=(p²+1)/(p²-1)

HOPE THIS MIGHT BE HELPFUL..

PLEASE MARK IT AS BRAINILIEST

Answer 2

Refer to the attachment