Question

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

Answer 1

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

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