Question

The value of $\tan 203°+\tan 22°+\tan 203°\tan 22°$ is

• A. $1$
• B. $-1$
• C. $2$
• D. $0$

Answer 1

The correct option is A

$1$

Finding the value of function:

Here we use the formula $\text{tan(A+B)=}\frac{\tan \text{A+tanB}}{1-\tan A\tan B}$

$\tan 225°=\tan (203°+22°)=\tan (180°+45°)=\tan {45}^{°}=1$

$$\begin{gathered} \tan (203°+22°)=\frac{\tan 203°+\tan 22°}{1-\tan 203°\tan 22°}=1 \\ \tan 203°+\tan 22°=1-\tan 203°\tan 22° \\ \tan 203°+\tan 22°+\tan 203°\tan 22°=1 \end{gathered}$$

Hence option(A) is the correct answer .