If \(\sin x + \cos x = \frac{1}{5}\) and \(0 < x < \pi,\) find \(\tan x.\)
+128460 sin x + cos x = 1/5 squrare both sides
sin^2x + 2sinxcosx + cos^2x = 1/25
(sin^2x +cos^2x ) + 2sin x cos x =1/25
1 + sin (2x) = 1/25
sin (2x ) = 1/25 - 1
sin (2x) = -24/25
Let 2x = A
So
arcsin (-24/25) = A ≈ -1.288 rads = pi + 1.288 rads ≈ 4.43 rads
So
2x = 4.43 rads
x = 2.215 rads
So tan (2.215) ≈ -1.33
