Question

Cos thita =root 3 sin theta find thetha

Answer 1

Answer:

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

3

sinθ=cosθ

⇒tan{\theta}=\frac{1}{\sqrt{3}}tanθ=

3

1

⇒{\theta}=30^{\circ}θ=30

∘

Thus, the value of the given expression is:

\frac{3cos^2{\theta}+2cos{\theta}}{3cos{\theta}+2}

3cosθ+2

3cos

2

θ+2cosθ

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

3cos30

∘

+2

3cos

2

30

∘

+2cos30

∘

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

3(

2

3

)+2

3(

4

3

)+2(

2

3

)

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

2(3

3

+4)

9+4

3