Question

if sinx+cosx =1/5 and 0≤x<π, then tanx is
please I want it step by step

Answer 1

Answer: -4/3 or 3/4

Step-by-step explanation:

given that

sin x + cos x =1/5

by squarring both the side

(sin x + cos x)² = 1/25

⇒sin²x+cos²x + 2sin x cos x=1/25

⇒1+sin 2x=1/25

⇒sin 2x =1/25 -1

⇒sin 2x = -24/25

as we know the triplet (24,7,25)

tan 2x = -24/7

$\frac{2tanx}{1+tan^{2}x}=\frac{-24}{7}\\\\14 tan x=-24-24 tan^{2}x$

by solving we get tan x = - 4/3 or 3/4