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  4. (1-2[cos 60°-cos 80°]/2 sin 10°)=......

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Q. $\frac{1-2\left[cos\,60^{\circ}-cos\,80^{\circ}\right]}{2\,sin\,10^{\circ}}=......$

MHT CETMHT CET 2019

Solution:

We have, $\frac{1-2\left(\cos 60^{\circ}-\cos 80^{\circ}\right)}{2 \sin 10^{\circ}}$
$=\frac{1-2\left(\frac{1}{2}-\cos 80^{\circ}\right)}{2 \sin 10^{\circ}}$
$=\frac{2 \cos 80^{\circ}}{2 \sin 10^{\circ}}$
$=\frac{\cos \left(90^{\circ}-10^{\circ}\right)}{\sin 10^{\circ}}$
$=\frac{\sin 10^{\circ}}{\sin 10^{\circ}}=1$