Question

find
if sin theta +1/sin theta -1 = root 3 + 2/ root 3-2
​

Answer 1

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

$\mathsf{\dfrac{sin\theta+1}{sin\theta-1}=\dfrac{\sqrt{3}+2}{\sqrt{3}-2}}$

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

$\textsf{The value of}\;\mathsf{\theta}$

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

$\mathsf{Consider}$

$\mathsf{\dfrac{sin\theta+1}{sin\theta-1}=\dfrac{\sqrt{3}+2}{\sqrt{3}-2}}$

$\textsf{This can be written as}$

$\mathsf{(sin\theta+1)(\sqrt{3}-2)=(sin\theta-1)(\sqrt{3}+2)}$

$\mathsf{\sqrt{3}sin\theta+\sqrt{3}-2sin\theta-2=\sqrt{3}sin\theta-\sqrt{3}+2\,sin\theta-2}$

$\mathsf{\sqrt{3}-2\,sin\theta=-\sqrt{3}+2\,sin\theta}$

$\mathsf{-4\,sin\theta=-2\sqrt{3}}$

$\mathsf{sin\theta=\dfrac{-2\sqrt{3}}{-4}}$

$\mathsf{sin\theta=\dfrac{\sqrt{3}}{2}}$

$\implies\boxed{\mathsf{\theta=\dfrac{\pi}{3}}}$

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