Rewrite as a sum?

Question

Rewrite as a sum: $6 (sin 5 θ) cos 2 θ$ $6(sin 5theta) cos 2 theta$

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Answer 1 · 2018-03-14T09:45:23

$\to 6 sin 5 x \cdot cos 2 x = 3 sin 7 x + 3 sin 3 x$ $rarr6sin5x*cos2x=3sin7x+3sin3x$

Use $\to 2 sin A \cdot cos B = sin (A + B) + sin (A - B)$ $rarr2sinA*cosB=sin(A+B)+sin(A-B)$

$\to 6 sin 5 x \cdot cos 2 x$ $rarr6sin5x*cos2x$

$= 3 \cdot [2 sin 5 x \cdot cos 2 x]$ $=3*[2sin5x*cos2x]$

$= 3 \cdot [sin (5 x + 2 x) + sin (5 x - 2 x)]$ $=3*[sin(5x+2x)+sin(5x-2x)]$

$= 3 \cdot [sin 7 x + sin 3 x] = 3 sin 7 x + 3 sin 3 x$ $=3*[sin7x+sin3x]=3sin7x+3sin3x$