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3.Trigonometrical Ratios, Functions and Identities
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The value of ,$\sqrt 3 \, cosec\, 20^o - sec\, 20^o $ is :
A
$2$
B
$\frac{{2\,\sin \,20^\circ }}{{\sin \,40^\circ }}$
C
$4$
D
$\frac{{4\,\sin \,20^\circ }}{{\sin \,40^\circ }}$
Solution
$\frac{{\sqrt 3 }}{{\sin {{20}^0}}}\,\, – \,\frac{1}{{\cos {{20}^0}}}$ $=$ $\frac{{2\left( {\frac{{\sqrt 3 }}{2}} \right)\,\,\cos {{20}^0}\,\, – \,\,\sin {{20}^0}}}{{\frac{{\sin {{40}^0}}}{2}}}$ $=$ $\frac{{\sin {{80}^0}\, + \,\sin {{40}^0}\,\, – \,\,\sin {{20}^0}}}{{\frac{{\sin {{40}^0}}}{2}}}$ $\frac{{2\,\sin {{30}^0}\,\cos {{50}^0}\,\, + \,\,\sin {{40}^0}}}{{\frac{{\sin {{40}^0}}}{2}}}$ $= 4$
Standard 11
Mathematics
