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

Question

Find the principal value of $\cot ^{-1}(\sqrt{3})$.

✓

Answer

cot^-1x represents an angle in (0, $\pi$) whose cotangent is x.
Let $x=\cot ^{-1}(\sqrt{3})$
$\Rightarrow \cot x=\sqrt{3}=\cot \left(\frac{\pi}{6}\right)$
$\Rightarrow x=\frac{\pi}{6}$
$\therefore$ Principal value of $\cot ^{-1}(\sqrt{3})$ is $\frac{\pi}{6}$.

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" 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

Determine the order and degree of the following differential equations. state also whether they are linear or non linear.
$\text{y}=\text{px}+\sqrt{\text{a}^2\text{p}^2+\text{b}^2},$ where $\text{p}=\frac{\text{dy}}{\text{dx}}$

Determine the order and degree of the following differential equations. state also whether they are linear or non linear.
$\frac{\text{d}^2\text{y}}{\text{dx}^2}+5\text{x}\Big(\frac{\text{dy}}{\text{dx}}\Big)-6\text{y}=\log\text{x}$

Integrate the functions in Exercises:
$\frac{\cos\sqrt{\text{x}}}{\sqrt{\text{x}}}$

Evaluate $\int_0^1 \frac{\left(x^2-x\right)}{\sqrt{x}} d x$.

Construct a 4 × 3 matrix whose element are:
$\text{a}_\text{ij}=\frac{\text{i}-\text{j}}{\text{i}+\text{j}}$

Classify 2 meters north-west measure as scalar and vector.

Evaluate the definite integral $\int_0^{\frac{\pi}{2}} \sin 2 x \tan ^{-1}(\sin x) d x$

The binary operation * : R x R $\rightarrow$ R is defined as a * b = 2a + b. Find (2 * 3) * 4.

Find the vector equation of the plane with intercepts $\text{3, -4 and 2 on } x, y \text{ and } z-\text{axis}$ respectively.

Define position vector of a point.