Question

What is the value of $\tan \left(-1575°\right)$?

• A. $1$
• B. $\frac{1}{2}$
• C. $0$
• D. $-1$

Answer 1

The correct option is A

$1$

Explanation of the correct option:

Find the value of $\tan (-1575°)$

$\begin{array}{rcl}\tan (-1575°)& =& -\tan \left(1575°\right)\mathbf{[}\mathbf{\because }\mathbf{}\mathbf{tan}\left(-\theta \right)\mathbf{=}\mathbf{-}\mathbf{tan}\mathbf{\theta }\mathbf{]}\\ & =& -\tan \left(4\times 360°+135°\right)\\ & =& -\tan \left(135°\right)\mathbf{[}\mathbf{\because }\mathbf{}\mathbf{tan}\mathbf{(}\mathbf{n}\mathbf{·}\mathbf{360}\mathbf{+}\mathbf{\theta }\mathbf{)}\mathbf{=}\mathbf{tan}\mathit{\theta }\mathbf{]}\\ & =& -\tan \left(90°+45°\right)\\ & =& -\left(-\cot \left(45°\right)\right)\mathbf{[}\mathbf{\because }\mathbf{}\mathbf{tan}\mathbf{(}\mathbf{90}\mathbf{+}\mathbf{\theta }\mathbf{)}\mathbf{=}\mathbf{-}\mathbf{cot}\mathit{\theta }\mathbf{]}\\ & =& -\left(-1\right)\mathbf{[}\mathbf{\because }\mathbf{cot}\mathbf{45}\mathbf{°}\mathbf{=}\mathbf{1}\mathbf{]}\\ & =& 1\end{array}$

Hence, the correct option is A.