Question

What is the value of $\tan \left(180-\theta \right)$?

Answer 1

Find the value of $\tan \left(180-\theta \right)$.

The value of the given expression is calculated as follows:
$$\begin{gathered} \tan \left(180°-\theta \right)=\tan \left[90°+\left(90°-\theta \right)\right] \\ \tan \left(180°-\theta \right)=-\cot \left(90°-\theta \right)\left[\because \tan \left(90°+\theta \right)=-\cot \theta \right] \\ \tan \left(180°-\theta \right)=-\tan \left(\theta \right)\left[\because \cot \left(90°-\theta \right)=\tan \theta \right] \end{gathered}$$
Hence, the value is $\tan \left(180°-\theta \right)=-\tan \left(\theta \right)$.