Question

Evaluate tan (-2025)​

Answer 1

The value of $tan(-2025)^{\circ}$ is $(-1)$.

Step-by-step explanation:

Now, $tan(-2025)^{\circ}$

$=-tan2025^{\circ}$

• We must know that, $tan(-\theta)=-tan\theta$.

• That is, the value of any negative angle of tan is also negative.

$=-tan(11\times 180^{\circ}+45^{\circ})$

$=-tan45^{\circ}$

• Here, the rule is $tan(n\pi+\theta)=tan\theta$, where $n$ is a Natural Number and $\theta$ an acute angle.

• That is when $\pi^{c}$ exixts as a multiple of any Natural Number, the value of tan comes in terms of the acute angle.

$=-1$

• since the value of $tan45^{\circ}$ is $1$

$\Rightarrow \boxed{tan(-2025)^{\circ}=-1}$

Answer 2

Here is the detailed answer.

Hope it will help you