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Home  >>  JEEMAIN and NEET  >>  Mathematics  >>  Trignometry

Find the value of $\sin(105^{\large\circ})$

$(a)\;\large\frac{\sqrt 3+1}{2}\qquad$$(b)\;\large\frac{\sqrt 3+1}{2\sqrt 2}$$\qquad(c)\;\large\frac{\sqrt 3-1}{\sqrt 2}$$\qquad(d)\;None\;of\;these$

1 Answer

$\sin(105^{\large\circ})=\sin[45^{\large\circ}+60^{\large\circ}]$
$\Rightarrow \sin 45^{\large\circ}\cos 60^{\large\circ}+\cos 45^{\large\circ}\sin 60^{\large\circ}$
$\Rightarrow \large\frac{1}{\sqrt 2}.\frac{\sqrt 3}{2}+\frac{1}{\sqrt 2}.\frac{\sqrt 3}{2}$
$\Rightarrow \large\frac{1+\sqrt 3}{2\sqrt 2}$
$\Rightarrow \large\frac{\sqrt 3+1}{2\sqrt 2}$
Hence (b) is the correct option.
answered Oct 9, 2013 by sreemathi.v
 

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