50^o + 50^o is equal to - Vidyadip

MCQ

$\sec {50^o} + \tan {50^o}$ is equal to

A
$\tan {20^o} + \tan {50^o}$
B
$2\tan {20^o} + \tan {50^o}$
✓
$\tan {20^o} + 2\tan {50^o}$
D
$2\tan {20^o} + 2\tan {50^o}$

✓

Answer

Correct option: C.

$\tan {20^o} + 2\tan {50^o}$

c
(c) $\sec {50^o} + \tan {50^o}$

==> $\tan ({70^o} - {20^o}) = \frac{{\tan {{70}^o} - \tan {{20}^o}}}{{1 + \tan {{70}^o}\tan {{20}^o}}}$

==> $\tan {50^o} + \tan {70^o}\tan {20^o}\tan {50^o} = \tan {70^o} - \tan {20^o}$

==> $\tan {50^o} + \tan {50^o} = \tan {70^o} - \tan {20^o}$

$[\,\because \tan {70^o} = \cot {20^o}]$

==> $2\tan {50^o} + \tan {20^o} = \tan {70^o}$

==> $2\tan {50^o} + \tan {20^o} = \tan {50^o} + \sec {50^o}$.

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