Find the value of the expression ^ - 1 ( 3 4 ). - Vidyadip

Question

Find the value of the expression ${\tan ^{ - 1}}\left( {\tan \frac{{3\pi }}{4}} \right)$.

✓

Answer

${\tan ^{ - 1}}\left( {\tan \frac{{3\pi }}{4}} \right)$
$ = {\tan ^{ - 1}}\left( {\tan \frac{{4\pi - \pi }}{4}} \right)$
$ = {\tan ^{ - 1}}\left[ {\tan \left( {\pi - \frac{\pi }{4}} \right)} \right]$
$ = {\tan ^{ - 1}}\left[ { - \tan \frac{\pi }{4}} \right]$
$ = {\tan ^{ - 1}}\tan \left( { - \frac{\pi }{4}} \right)$
$ = - \frac{\pi }{4}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "1 Marks Question" from Inverse Trigonometric Functions→Inverse Trigonometric Functions — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Find the equation of normal at point $(1,2)$ on the curve $y=x^2+1$.

If vectors $\vec{a}=\hat{i}-2 \hat{j}+\hat{k}, \vec{b}=2 \hat{i}+4 \hat{j}+5 \hat{k}$ and $\vec{c}=\hat{i}+6 \hat{j}+7 \hat{k}$ then find the sum of vectors.

Prove that the function given by f(x) = cos x is decreasing in (0, $\pi$).

Find the maximum and minimum values of f, if any, of the function given by f(x) = | x |, x $\in$ R.

Find the interval of the function that is strictly increasing or decreasing: $10 - 6x - 2x^2$

Write the position vector of the point which divides the join of points with position vectors $3\overrightarrow{\text{a}} - 2\overrightarrow{\text{b}} \text{and } 2\overrightarrow{\text{a}} + 3\overrightarrow{\text{b}}$ in the ratio $2:1.$

If f(x) is differentiable at x = c, then write the value of $\text{f}\lim_\limits{\text{x}\rightarrow{\text{c}}}\text{f(x)}.$

Write the differential equation representing the family of curves y = mx, where m is an arbitrary constant.

Determine order and degree (if defined) of differential equation: $y" + (y')^2 + 2y = 0$

Evaluate the following:
$\sin^{-1}(\sin12)$