Download App

Inverse Trigonometric Functions — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsInverse Trigonometric Functions2 Marks
Question
Evaluate the following:
$\cot\Big(\cot^{-1}\frac{3}{5}\Big)$
✓

Answer

Let $\cot\Big(\cot^{-1}\frac{3}{5}\Big)=\text{y}$ where $\text{y}\in \Big[0,\frac{\pi}{2}\Big]$
$\Rightarrow \cos \text{y}=\frac{3}{5}$
$\cot \Big(\cos^{-1}\frac{3}{5}\Big)=\cot\text{y}$
To fing:
$\Rightarrow \text{As}\ 1+\tan^2\theta=\sec^2\theta$
$\Rightarrow \tan \text{y}=\sqrt{\sec^2\text{y}-1}$ where $\text{y}\in \Big[0, \frac{\pi}{2}\Big]$
$\Rightarrow \frac{1}{\cot\text{y}}=\sqrt{\Big(\frac{1}{\cos^2\text{y}}\Big)-1}$
$\Rightarrow \frac{1}{\cot\text{y}}=\sqrt{\Big(\frac{5}{3}\Big)^2-1}$
$\Rightarrow \frac{1}{\cot\text{y}}=\sqrt{\frac{16}{9}}$
$\Rightarrow \cot\text{y}=\frac{3}{4}$
$\Rightarrow \cot\Big(\cos^{-1}\frac{3}{5}\Big)=\frac{3}{4}$

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 "Solve the Following Question.(2 Marks)" from Inverse Trigonometric Functions→Inverse Trigonometric Functions — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Evaluate: $\int e^x\left[\frac{\sqrt{1-x^2} \sin ^{-1} x+1}{\sqrt{1-x^2}}\right] d x$
→
Diffrentiate the following w. r. t. x

$\sin ^{-1}\left(\frac{1-x^2}{1+x^2}\right)$

→
Using truth tables prove the following logical equivalences. ~(p ∨ q) ∨ (~p ∧ q) ≡ ~p
→
If $\vec{\text{a}}=3\hat{\text{i}}-\hat{\text{j}}+2\hat{\text{k}}$ and $\vec{\text{b}}=2\hat{\text{i}}+\hat{\text{j}}-\hat{\text{k}},$ then find $\big(\vec{\text{a}}\times\vec{\text{b}}\big)\vec{\text{a}}.$
→
Evaluate the following:

$\int_0^1\left(\frac{1}{1+x^2}\right) \sin ^{-1}\left(\frac{2 x}{1+x^2}\right) d x$

→
If a line makes angles $\alpha, \beta, \gamma$ with co-ordinate axes prove that $\cos 2 \alpha+\cos 2 \beta+\cos 2 \gamma+1=0$
→
Show that $f(x) = x^3 - 15x^2 + 75x - 50$ is an increasing function for all $\text{x}\in\text{R}.$
→
Find the general solution of : $\sin \theta=\frac{\sqrt{3}}{2}$
→
Let f be a real function given by $\text{f(x)}=\sqrt{\text{x}-2}.$ Find the following:
$f^2$
Also, show that fof $\neq f^2​​​​​​​$​​​​​​​.
→
Find $\frac{d y}{d x}$, if $y=(\log x)^x$
→