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Mashcka [7]
4 years ago
8

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

Mathematics
1 answer:
givi [52]4 years ago
5 0
(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

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