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Find the value :$\sin 75^{\large\circ}$

$\begin{array}{1 1}(A)\;\large\frac{\sqrt 3+1}{2\sqrt 2}\\(B)\;\large\frac{\sqrt 3-1}{2\sqrt 2}\\(C)\;\large\frac{\sqrt 2+1}{2\sqrt 2}\\(D)\;\large\frac{\sqrt 2-1}{2\sqrt 2}\end{array} $

1 Answer

Toolbox:
  • $\sin (A+B)=\sin A\cos B+\cos A\sin B$
$\sin(45^{\large\circ}+30^{\large\circ})=\sin 45^{\large\circ}\cos 30^{\large\circ}+\cos 45^{\large\circ}.\sin 30^{\large\circ}$
$\Rightarrow \large\frac{1}{\sqrt 2}.\frac{\sqrt 3}{2}$$+\large\frac{1}{\sqrt 2}.\frac{1}{2}$
$\Rightarrow \large\frac{\sqrt 3+1}{2\sqrt 2}$
Hence (A) is the correct answer.
answered Apr 17, 2014 by sreemathi.v
 
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