Question

1+sin^x=3sinxcosx than tan x=1 or1/2

Answer 1

sin^x ?

Answer 2

perhaps you meant sin^2 x ? please confirm

Answer 3

1+sin^2x=3sinxcosx
cos^2x+sin^2x+sin^2x=3sinxcosx (cos^2x+sin^2x=1)
cos^2 x+2 sin^2 x=3sinxcosx
Divide by cos^2 x,
1+2 tan^2 x=3 tan x
2 tan^2 x -3 tan x+1=0
2tan^2 x-2tanx-tanx+1=0
2tanx(tanx-1)-1(tanx-1)=0
(tanx-1)(2tanx-1)=0
tanx-1=0,tanx=1 or2tanx-1=0,2tanx=1,tanx=1/2