Question #b2380

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Question #b2380

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Answer 1 · 2016-12-10T19:13:02

$sin (x) + sin (7 x) = 2 sin (4 x) cos (3 x)$ $sin(x)+sin(7x)=2sin(4x)cos(3x)$

Explanation:

Using the formula

$sin (α) + sin (β) = 2 sin (\frac{α + β}{2}) cos (\frac{α - β}{2})$ $sin(alpha)+sin(beta) = 2sin((alpha+beta)/2)cos((alpha-beta)/2)$

we have

$sin (x) + sin (7 x) = 2 sin (\frac{x + 7 x}{2}) cos (\frac{x - 7 x}{2})$ $sin(x)+sin(7x) = 2sin((x+7x)/2)cos((x-7x)/2)$

$= 2 sin (\frac{8 x}{2}) cos (- \frac{6 x}{2})$ $=2sin((8x)/2)cos(-(6x)/2)$

$= 2 sin (4 x) cos (- 3 x)$ $=2sin(4x)cos(-3x)$

$= 2 sin (4 x) cos (3 x)$ $=2sin(4x)cos(3x)$

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Question #b2380

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