Question

Express root 3 sin theta + cos theta as a Sin of an angle ​

Answer 1

I hope this will help you.

Answer 2

given : $\sqrt{3}\sin \theta +\cos\theta$

we have to express it in the form of sin only

therefore ,

$\sqrt{3}\sin \theta +\cos\theta \\\\\text{multiply and divide by }\\\\\sqrt{(3)^2+(1)^2}\\\\we get \\\\(\frac{\sqrt{3}\sin \theta}{\sqrt{(3)^2+(1)^2}}+\frac{\cos\theta}{\sqrt{(3)^2+(1)^2}})\times \sqrt{(3)^2+(1)^2}$

$(\frac{\sqrt{3}}{\sqrt{4}}\sin\theta +\frac{1}{\sqrt{4}}\cos\theta)\times \sqrt{4}\\\\2\left ( \frac{\sqrt{3}}{2}\sin\theta+\frac{1}{2}\cos\theta \right )\\\\2\left ( \sin\theta \cos \frac{\pi}{6}+\cos\theta \sin \frac{\pi}{6} \right )\\\\\sin A \cos B + \cos A \sin B = \sin (A+B)\\\\2\sin (\theta+\frac{\pi}{6})$

hence ,

$\sqrt{3}\sin \theta +\cos\theta = 2\sin (\theta+\frac{\pi}{6})$

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