The value of 70^o + 470^o is - Vidyadip

MCQ

The value of $\cot {70^o} + 4\cos {70^o}$ is

A
$\frac{1}{{\sqrt 3 }}$
✓
$\sqrt 3 $
C
$2\sqrt 3 $
D
$\frac{1}{2}$

✓

Answer

Correct option: B.

$\sqrt 3 $

b
(b) Now, $\cot {70^o} + 4\cos {70^o} = \frac{{\cos {{70}^o} + 4\sin {{70}^o}\cos {{70}^o}}}{{\sin {{70}^o}}}$

$ = \frac{{\cos {{70}^o} + 2\sin {{140}^o}}}{{\sin {{70}^o}}} $

$= \frac{{\cos {{70}^o} + 2\sin ({{180}^o} - {{40}^o})}}{{\sin {{70}^o}}}$

$ = \frac{{\sin {{20}^o} + \sin {{40}^o} + \sin {{40}^o}}}{{\sin {{70}^o}}} $

$= \frac{{2\sin {{30}^o}\cos {{10}^o} + \sin {{40}^o}}}{{\sin {{70}^o}}}$

$ = \frac{{\sin {{80}^o} + \sin {{40}^o}}}{{\sin {{70}^o}}} $

$= \frac{{2\sin {{60}^o}\cos {{20}^o}}}{{\sin {{70}^o}}} = \sqrt 3 $.

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