Question

If $\cos ecA+cotA=11/2$, then $\tan A=?$

• A. $21/22$
• B. $15/16$
• C. $44/117$
• D. $117/43$

Answer 1

The correct option is C

$44/117$

The explanation for the correct option:

Step 1. Using the identity $\mathit{c}\mathit{o}\mathit{s}\mathit{e}{\mathit{c}}^{\mathbf{2}}\mathit{A}\mathbf{}\mathbf{–}\mathbf{}\mathit{c}\mathit{o}{\mathit{t}}^{\mathbf{2}}\mathit{A}\mathbf{}\mathbf{=}\mathbf{}\mathbf{1},$

Given, $\cos ecA+cotA=11/2\dots .\left(i\right)$

$\begin{array}{rcl}& \Rightarrow & (\cos ecA+cotA)(\cos ecA–cotA)=1\\ (11/2)(\cos ecA–cotA)& =& 1\\ \cos ecA–cotA& =& 2/11\dots .\left(ii\right)\end{array}$

Step 2. Subtracting (ii) from (i),

$\begin{array}{rcl}\cos ecA+cotA–\cos ecA+cotA& =& (11/2)–(2/11)\\ 2cotA& =& \frac{(121–4)}{22}\\ cotA& =& 117/44\\ \tan A& =& \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$cotA$}\right.\\ & =& \raisebox{1ex}{$\mathbf{44}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{117}$}\right.\end{array}$

Hence, The correct answer is option (C).