Question

SecQ-tanQ=P so find the velu of cosQ

Answer 1

We know sec²x - tan²x = 1

so, sec²Q - tan²Q = 1

or, (secQ - tanQ)(secQ - tanQ) = 1

or, (secQ - tanQ) = 1/(secQ + tanQ) = 1/P

now, solve equations ; secQ + tanQ = P and secQ - tanQ = 1/P

e.g., (secQ - tanQ) + (secQ + tanQ) = p + 1/p

2secQ = (p² + 1)/p

secQ = (p² + 1)/2p

cosQ = 2p/(p² + 1) = base/hypotenuse

perpendicular =

= ±(p² - 1)

so, cosecQ = hypotenuse/perpendicular

= ± (p² + 1)/(p² - 1)