Download App

INVERSE TRIGNOMETRIC FUNCTIONS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsINVERSE TRIGNOMETRIC 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 "2 Marks" from INVERSE TRIGNOMETRIC FUNCTIONS→INVERSE TRIGNOMETRIC FUNCTIONS — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Evaluate the definite integral in Exercise:

$\int\limits_0^{\frac{\pi}{4}}\sin2\text{x}\ \text{dx}$

→
Evaluate the determinants.
  1. $\begin{vmatrix}\cos\theta&-\sin\theta\\\sin\theta&\cos\theta\end{vmatrix}$
  2. $\begin{vmatrix}x^2-x+1&x-1\\x+1&x+1\end{vmatrix}$
→
Show that $\left( {\vec a - \vec b} \right) \times \left( {\vec a + \vec b} \right) = 2\left( {\vec a \times \vec b} \right)$
→
If A and B are square matrices of the same order such that |A| = 3 and AB = I, then write the value of |B|.
→
Find the vector equation one of following plane.
2x - y + 2z = 8
→
Find the second order derivatives of the function given in Exercise:
$\log(\log\text{x})$
→
Evaluate the following integrals:
$\int\text{x}^{\frac{5}{4}}\text{dx}$
→
If $\vec{\text{a}}=\hat{\text{i}}+2\hat{\text{j}},\ \vec{\text{b}}=\hat{\text{j}}+2\hat{\text{k}}$, write a unit vector along the vector $3\vec{\text{a}}-2\vec{\text{b}}$.
→
Integrate the function: sec2 (7 – 4x)
→
For the principal values of the following:
$\cot^{-1}\Big(\sqrt3\Big)$
→