Question

If root3 sin theta=cos theta then find the value of 3cos ​2 ​​theta + 2cos​ theta/ 3costheta +2

Answer 1

Answer:

Step-by-step explanation:

this will help you a lot

Answer 2

Answer:

$\text{The value is }\frac{9+4\sqrt3}{8+6\sqrt3}$

Step-by-step explanation:

Given that

$\sqrt3\sin \theta=\cos \theta$

$\tan \theta=\frac{1}{\sqrt3}$

$\theta=30^{\circ}$

$\frac{3\cos^2\theta+2\cos\theta}{3\cos\theta+2}\\\\=\frac{3\cos^230+2\cos30}{3\cos30+2}\\\\=\frac{3(\frac{\sqrt3}{2})^2+2(\frac{\sqrt3}{2})}{3(\frac{\sqrt3}{2})+2}\\\\=\frac{3(\frac{9}{4})+\sqrt3}{3(\frac{\sqrt3}{2})+2}\\\\=\frac{9+4\sqrt3}{8+6\sqrt3}$

$\text{The value is }\frac{9+4\sqrt3}{8+6\sqrt3}$