Question

If sec x + tan x = p, then find the value of sin x ?

Answer 1

so sec x + tan x = p
1 + sin x = p * cos x

square on both sides...
1 + sin^2 x + 2 sin x =  p^2  (1 - sin^2 x)
(1+p^2) sin^2 x + 2 sin x +1 - p^2 = 0

Sin x = [ - 1 +- p^2 ] /(1+p^2)    = -1  or  (p^2 -1)/(p^2+1)
if p =0,  sin x = -1
otherwise,  sin x = (p^2-1)/(p^2+1)