Question

The value of $\tan \left(-945°\right)$ is

• A. $-1$
• B. $-2$
• C. $-3$
• D. $-4$

Answer 1

The correct option is A

$-1$

Explanation for the correct option

The given trigonometric expression: $\tan \left(-945°\right)$.

$$\begin{gathered} \tan \left(-945°\right)=-\tan \left(945°\right)\left[\because \tan \left(-\theta \right)=-\tan \left(\theta \right)\right] \\ \Rightarrow \tan \left(-945°\right)=-\tan \left(900°+45°\right) \\ \Rightarrow \tan \left(-945°\right)=-\tan \left[\left(5\times 180°\right)+45°\right] \\ \Rightarrow \tan \left(-945°\right)=-\tan \left(45°\right)\left[\because \tan \left\{\left(2n+1\right)180°+\theta \right\}=\tan \left(\theta \right)\right] \\ \Rightarrow \tan \left(-945°\right)=-1 \end{gathered}$$

Hence, option A is correct.