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The value of expression $\large\frac{1-4\sin 10^{\large\circ}\sin 70^{\large\circ}}{2\sin 10^{\large\circ}}$

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

1 Answer

Given expression is $\large\frac{1-4\sin 10^{\large\circ}\sin 70^{\large\circ}}{2\sin 10^{\large\circ}}$
$\Rightarrow \large\frac{1-2[\cos 60^{\large\circ}-\cos 80^{\large\circ}]}{2\sin 10^{\large\circ}}$
$\Rightarrow \large\frac{1-2[\large\frac{1}{2}-\cos 80^{\large\circ}]}{2\sin 10^{\large\circ}}$
$\Rightarrow \large\frac{2\cos 80^{\large\circ}}{2\sin 10^{\large\circ}}$
$\Rightarrow \large\frac{\cos (90^{\large\circ}-10^{\large\circ})}{\sin 10^{\large\circ}}$
$\Rightarrow \large\frac{\sin 10^{\large\circ}}{\sin 10^{\large\circ}}$
$\Rightarrow 1$
Hence (b) is the correct answer.
answered Oct 9, 2013 by sreemathi.v
 
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