For the principal value, evaluate [ ^ -1 ( ^ -1 1 ) ] - Vidyadip

Question

For the principal value, evaluate $\cot \left[\sin ^{-1}\left\{\cos \left(\tan ^{-1} 1\right)\right\}\right]$

✓

Answer

We know that $\tan ^{-1} 1=\frac{\pi}{4}$
$\therefore \cot \left[\sin ^{-1}\left\{\cos \left(\tan ^{-1} 1\right)\right\}\right]$
$=\cot \left\{\sin ^{-1}\left(\cos \frac{\pi}{4}\right)\right\}$
$=\cot \left(\sin ^{-1} \frac{1}{\sqrt{2}}\right)$
$=\cot \frac{\pi}{4}$
$=1$

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 "2 Marks Questions" from Model Paper 4→Model Paper 4 — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

For the principal values of the following:
$\cot^{-1}\Big(\sqrt3\Big)$

If $f : R → $R be defined by $f(x) = x^4$, write $f^{-1}(1).$

Write the ratio in which the line segment joining (a, b, c) and (-a, -b, -c) is divided by the xy-plane.

Differentiate the $\sin \left( {{{\tan }^{ - 1}}{e^{ - x}}} \right)$ w.r.t. x.

Let A and B be two independent events such that $P(A) = p_1$ and $P(B) = p_2$. Describe in words the events whose probabilities are:
$(1 - p_1)p_2$.

If $\text{A}=\begin{bmatrix}1&2\\3&-1\end{bmatrix}$ and $\text{B}=\begin{bmatrix}1&0\\-1&0\end{bmatrix},$ find |AB|.

If $\text{f(x)}=\log_\text{e}(\log_\text{e}\text{x}),$ then write the value of f'(e).

If $\vec{\text{a}}=\hat{\text{i}}-\hat{\text{j}}$ and $\vec{\text{b}}=-\hat{\text{j}}+2\hat{\text{k}},$ find $\big(\vec{\text{a}}-2\vec{\text{b}}\big).\big(\vec{\text{a}}+\vec{\text{b}}\big).$

For the principal values, evaluate the following:
$\tan^{-1}\Big\{2\sin\Big(4\cos^{-1}\frac{\sqrt3}{2}\Big)\Big\}$

If $\text{A}=\begin{bmatrix}2&3\\5&7\end{bmatrix},\text{ B}=\begin{bmatrix}-1&0&2\\3&4&1\end{bmatrix},\text{C}=\begin{bmatrix}-1&2&3\\2&1&0\end{bmatrix},$ find
A + B and B + C