Question

3(sin2x+cos2x)+3(3−sin2x−cos2x)=28
show that either cos x = 0 or tan x = –1.

Answer 1

hi! does sin2x mean sin2x or sin^2 x?

Answer 2

sin2x

Answer 3

\[3\sin2x + 3\cos2x +3(1-\cos 2x-\sin 2x +2);
3\sin2x +3\cos 2x+3(2\sin^2 x-\sin2x+2);
3\sin2x+3\cos^2x-3\sin^2 x+6\sin^2 x-3\sin2x+6=28;
3\cos^2 x+3\sin^2 x=22;
Divide by \cos^2 x,
3+3\tan^2 x= 223\tan^2 x +3= 22+22 \tan^2 x;
19=19\tan^2 x;
tan x =-1.\]