Question

Evaluate: $\frac{\tan {35}^{\circ }}{\cot {55}^{\circ }}+\frac{\cot {78}^{\circ }}{\tan {12}^{\circ }}=$

• A. $0$
• B. $1$
• C. $2$
• D. None of these

Answer 1

The correct option is C $2$

Given expression is $\frac{\tan {35}^o}{\cot {55}^o}+\frac{\cot {78}^o}{\tan {12}^o}$

We can rewrite the expression as:

$\frac{\tan {35}^o}{\cot \left({90}^o-{35}^o\right)}+\frac{\cot {78}^o}{\tan \left({90}^o-78\right)}$

We know that, $\cot ({90}^o-\theta )=\tan \theta$ and $\tan ({90}^o-\theta )=\cot \theta$

$\therefore$ The expression becomes,

$\frac{\tan {35}^o}{\tan {35}^o}+\frac{\cot {78}^o}{\cot {78}^o}$

$\Rightarrow 1+1$

$\Rightarrow 2$

Hence, $\frac{\tan {35}^o}{\cot {55}^o}+\frac{\cot {78}^o}{\tan {12}^o}=2$