Download App

Inverse Trigonometric Functions — Maths STD 12 Science — Question

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

Answer

$\text{cosec}\Big\{\cot^{-1}\Big(-\frac{12}{5}\Big)\Big\}$
$=\text{cosec}\Big\{-\cot^{-1}\Big(\frac{12}{5}\Big)\Big\}$ $\big[\because\ \cot^{-1}(\text{x})=-\cot^{-1}(\text{x})\big]$
$=\text{cosec}\Big\{-\text{cosec}^{-1}\Big(\frac{13}{12}\Big)\Big\}$
$\Big[\therefore\ \cot^{-1}\Big(\frac{\text{b}}{\text{p}}\Big)=\text{cosec}^{-1}\Big(\frac{\text{h}}{\text{p}}\Big)\Big]$
$=\text{cosec}\Big\{\text{cosec}^{-1}\Big(\frac{13}{12}\Big)\Big\}$ $\big[\because\ \text{cosec}(-\text{x})=-\text{cosec}(\text{x})\big]$
$=-\frac{13}{12}$

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

Differentiate the following w. r. t. x.$y=\left(x^3+2 x-3\right)^4(x+\cos x)^3$
→
Diffrentiate the following w. r. t. x

$\tan ^{-1}\left(\frac{2 x^{\frac{5}{2}}}{1-x^5}\right)$

→
Find the cofactors of the elements for the matrix $\left[\begin{array}{ll}-1 & 2 \\ -3 & 4\end{array}\right]$
→
Let $A=\left[a_{i j}\right]$ be a square matrix of order $3 \times 3$ and $C_{i j}$ denote cofactor of $a_{i j}$ in $A$. if $|A|=5$, write the value of $a_{13} C_{13}+$ $a_{23} C_{23}+a_{33} C_{33}$.
→
Evaluate the following integrals:
$\int\frac{1}{3\sqrt{\text{x}^2}}\text{dx}$
→
Integrate the following functions w.r.t. x:

$\sqrt{(x-3)(7-x)}$

→
Evaluate the following:
$\tan\Big(\cos^{-1}\frac{8}{17}\Big)$
→
If A = {1, 2, 3, 4} define relations on A which have properties of being:
Reflexive, symmetric and transitive.
→
Integrate the following functions w.r.t. x:
$\frac{1+x}{x-\sin (x+\log x)}$
→
Integrate the following functions w. r. t. x

$\int \frac{1}{4-5 \cos x} \cdot d x$

→