Question

1. If sec x + tan x = 3/2 and 0 ≤ x ≤ pi/2 then the value of sin x is...

2. If 0 ≤ x ≤ pi/2 and tan²x + sec x = 5 then cos x = ...

Please help

Answer 1

secx + tanx = 3/2
secx = 3/2 - tanx
sec^2 x = 9/4 - 3tanx + tan^2 x
tan^2 x + 1 = 9/4 - 3tanx
tanx = 5/12
so, sinx = 5/13

#2 is quite similar.

tan^2 x + secx = 5
sec^2 x - 1 + secx = 5
sec^2 x + secx - 6 = 0
(secx+3)(secx-2) = 0
in QI, then, cosx = 1/2