Question

if root 3 sin theta = cos theta, then the value of 3 cos square theta + 2 cos theta upon 3 cos theta + 2 is equal to
(i)root 3 cos theta
(ii)3 sin theta
(iii)3 cos theta
(iv)root 3 sin theta​

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{\sqrt{3}\,sin\theta=cos\theta}$

$\underline{\textbf{To find:}}$

$\textsf{The value of}$

$\mathsf{\dfrac{3\,cos^2\theta+2\,cos\theta}{3\,cos\theta+2}}$

$\underline{\textbf{Solution:}}$

$\mathsf{Consider,}$

$\mathsf{\dfrac{3\,cos^2\theta+2\,cos\theta}{3\,cos\theta+2}}$

$\mathsf{=\dfrac{cos\theta(3\,cos\theta+2)}{3\,cos\theta+2}}$

$\mathsf{=cos\theta}$

$\mathsf{=\sqrt{3}\,sin\theta}$

$\underline{\textbf{Answer:}}$

$\mathsf{Option\;(iv)\;is\;correct}$

$\underline{\textbf{Find more:}}$

If cosec thete =root 5 : find the value of 2- sin square theta - cos Square theta

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