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Questions  >>  CBSE XI  >>  Math  >>  Trigonometric Functions
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Q)

The value of $\sin\large\frac{\pi}{10}$$\sin\large\frac{13\pi}{10}$ is

$\begin{array}{1 1}(A)\;\large\frac{1}{2}&(B)\;\large\frac{-1}{2}\\(C)\;\large\frac{-1}{4}&(D)\;1\end{array} $

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A)
Toolbox:
  • $\sin 18^{\large\circ}=\large\frac{\sqrt 5-1}{4}$
  • $\cos 36^{\large\circ}=\large\frac{\sqrt 5+1}{4}$
$\sin\large\frac{\pi}{10}$$\sin\large\frac{13\pi}{10}$
$\sin\large\frac{180}{10}$$\sin\large\frac{13(180)}{10}$
$\Rightarrow \sin 18^{\large\circ}.\sin 234^{\large\circ}$
$\Rightarrow \sin 18^{\large\circ}.\sin (\large\frac{3\pi}{2}$$+36)^{\large\circ}$
$\Rightarrow \sin 18^{\large\circ}\cos 36^{\large\circ}$
$\Rightarrow -\large\frac{\sqrt 5-1}{4}\times \large\frac{\sqrt 5+1}{4}$
$\Rightarrow -\large\frac{1}{4}$
Hence (C) is the correct answer.
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