Download App

Inverse Trigonometric Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsInverse Trigonometric Functions2 Marks
Question
Evaluate the following:
$\sec^{-1}\Big(\sec\frac{5\pi}{4}\Big)$
✓

Answer

We have
$\sec^{-1}\Big(\sec\frac{5\pi}{4}\Big)$
$=\sec^{-1}\Big(\sec\Big(\pi+\frac{\pi}{4}\Big)\Big)$
$=\sec^{-1}\Big(-\sec\Big(\frac{\pi}{4}\Big)\Big)$
$=\sec^{-1}\big(-\sqrt2\big)$
$=\frac{3\pi}{4}$

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 "2 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

Find the vector equation of a plane which is at a distance of 5 unit from the origin and which is normal to the vector $\hat{\text{i}}-2\hat{\text{j}}-2\hat{\text{k}}$
→
If I3 denotes identity matrix of order 3 × 3, write the value of its determinant.
→
If $\vec{\text{a}}$ and $\vec{\text{b}}$ are vectors of equal magnitude, write the value of $\big(\vec{\text{a}}+\vec{\text{b}}\big).\big(\vec{\text{a}}-\vec{\text{b}}\big).$
→
If $\text{P}=\begin{bmatrix}\text{x}&0&0\\0&\text{y}&0\\0&0&\text{z}\end{bmatrix}$ and $\text{Q}=\begin{bmatrix}\text{a}&0&0\\0&\text{b}&0\\0&0&\text{c}\end{bmatrix},$ then prove that $\text{PQ}=\begin{bmatrix}\text{xa}&0&0\\0&\text{yb}&0\\0&0&\text{zc}\end{bmatrix}=\text{QP}.$
→
Evaluate the following determinant:
$\begin{vmatrix}\text{a}&\text{h}&\text{g}\\\text{h}&\text{b}&\text{f}\\\text{g}&\text{f}&\text{c}\end{vmatrix}$
→
Evaluate the following integrals:
$\int\limits^{1.5}_0\big[\text{x}\big]\text{dx}$
→
Find the second order derivatives of the function given in Exercise:
$\text{x}^3\log\text{x}$
→
If $\text{x}=2\text{ at},\text{y}=\text{at}^2,$ where a is a constant, then find $\frac{\text{d}^2\text{y}}{\text{dx}^2}\text{ at}\text{ x}=\frac{1}{2}.$
→
Evaluate the following:
$\text{cosec}\Big(\cos^{-1}\frac{3}{5}\Big)$
→
Let f : R → R and g : R → R be defined by f(x) = x2 and g(x) = x + 1. Show that fog ≠ gof.
→