Question

If $A=35°,B=15°$then $C=40°,$then $\tan A\tan B+\tan B\tan C+\tan C\tan A$ is equal to

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

The correct option is B

$1$

Explanation for the correct option:

Step 1. Finding the value:

Given, $A=35°,B=15°,C=40°$

,$\begin{array}{rcl}A+B+C& =& 35°+15°+40°\\ & =& 90°\end{array}$

Step 2. Taking “tan” on both sides,

$\tan (A+B+C)=\tan 90°$

$\Rightarrow$ $\tan (A+B)\tan C=1$

$\Rightarrow$ $\left[\frac{(\tan A+\tan B)}{(1–\tan A\tan B)}\right]\tan C=1$

$\Rightarrow$ $(\tan A+\tan B)\tan C=1–\tan A\tan B$

$\Rightarrow$$\mathit{t}\mathit{a}\mathit{n}\mathbf{}\mathit{A}\mathbf{}\mathit{t}\mathit{a}\mathit{n}\mathbf{}\mathit{C}\mathbf{}\mathbf{+}\mathbf{}\mathit{t}\mathit{a}\mathit{n}\mathbf{}\mathit{B}\mathbf{}\mathit{t}\mathit{a}\mathit{n}\mathbf{}\mathit{C}\mathbf{}\mathbf{+}\mathbf{}\mathit{t}\mathit{a}\mathit{n}\mathbf{}\mathit{A}\mathbf{}\mathit{t}\mathit{a}\mathit{n}\mathbf{}\mathit{B}\mathbf{}\mathbf{=}\mathbf{}\mathbf{1}$

Hence, Option ‘B’ is Correct.