Question

2 sin 5 theta into cos theta​

Answer 1

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Answer 2

Answer:

Required value of 2 sin 5 theta into cos theta is $\sin(6\theta) + \sin(4\theta)$

Step-by-step explanation:

Given,

$2 \sin(5\theta) \times \cos(\theta)$

We know,

$\sin(a + b) = \sin(a) \cos(b) + \cos(a) \sin(b) \\ \sin(a - b) = \sin(a) \cos(b) - \cos(a) \sin(b)$

Here,

$2 \sin(5\theta) \times \cos(\theta) \\ = \sin(5\theta) \cos(\theta) + \sin(5\theta) \cos(\theta)$

$= \sin(5\theta) \cos(\theta) + \cos(5\theta) \sin(\theta) + \sin(5\theta) \cos(\theta) - \cos(5\theta) \sin(\theta)$

$= \sin(5 \theta + \theta) + \sin(5\theta - \theta) \\ = \sin(6\theta) + \sin(4\theta)$

Some more important Trigonometry formulas,

$sin(x) = \cos(\frac{\pi}{2} - x) \\ \tan(x) = \cot(\frac{\pi}{2} - x) \\ \sec(x) = \csc(\frac{\pi}{2} - x) \\ \cos(x) = \sin(\frac{\pi}{2} - x) \\ \cot(x) = \tan(\frac{\pi}{2} - x) \\ \csc(x) = \sec(\frac{\pi}{2} - x)$

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