Question

Show that (3cosx+sinx) (cosx+3sinx)=3+5sin2x

Answer 1

`(3 \cos x+ \sin x) (\cos x+3\sin x) = \\ \\ = 3 \cos^(2) x + 9 \cos x \sin x + \cos x \sin x + 3 \sin ^(2) x = \\ \\ = 10 \cos x \sin x +3 \underbrace{(\sin ^(2) x + \cos ^(2) x)}_(=1) =\boxed{5 \sin x + 3 }`

---------------------------------------------------------


`\sin (2x) = 2 \cos x \sin x`