Question

If 3 sin theta = cos theta, find the value of
3 cos square theta+ 2 cos theta
$\div$

3 cos theta +2​

Answer 1

Answer:

Step-by-step explanation:

It is given that \sqrt{3}sin\theta=cos{\theta}3sinθ=cosθ

⇒tan{\theta}=\frac{1}{\sqrt{3}}tanθ=31

⇒{\theta}=30^{\circ}θ=30∘

Thus, the value of the given expression is:

\frac{3cos^2{\theta}+2cos{\theta}}{3cos{\theta}+2}3cosθ+23cos2θ+2cosθ

=\frac{3cos^230^{\circ}+2cos30^{\circ}}{3cos30^{\circ}+2}3cos30∘+23cos230∘+2cos30∘

=\frac{3(\frac{3}{4})+2(\frac{\sqrt{3}}{2})}{3(\frac{\sqrt{3}}{2})+2}3(23)+23(43)+2(23)

=\frac{9+4\sqrt{3}}{2(3\sqrt{3}+4)}2(33+4)9+43

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Answer 2

Answer:

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Step-by-step explanation:

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