JEE Mains · Maths · STD 12 - 2. inverse trigonometric function
The value of \(\tan ^{-1}\left(\frac{\cos \left(\frac{15 \pi}{4}\right)-1}{\sin \left(\frac{\pi}{4}\right)}\right)\) is equal to
- A \(-\frac{\pi}{4}\)
- B \(-\frac{\pi}{8}\)
- C \(-\frac{5 \pi}{12}\)
- D \(-\frac{4 \pi}{9}\)
Answer & Solution
Correct Answer
(B) \(-\frac{\pi}{8}\)
Step-by-step Solution
Detailed explanation
\(\tan ^{-1}\left[\frac{\cos \left(4 \pi-\frac{\pi}{4}\right)-1}{\sin \frac{\pi}{4}}\right] \Rightarrow \tan ^{-1}\left(\frac{\cos \frac{\pi}{4}-1}{\sin \frac{\pi}{4}}\right)\) \(\tan ^{-1}\left(\frac{1-\sqrt{2}}{1}\right)=-\frac{\pi}{8}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- Let \(\frac{\sin \mathrm{A}}{\sin \mathrm{B}}=\frac{\sin (\mathrm{A}-\mathrm{C})}{\sin (\mathrm{C}-\mathrm{B})}\), where \(\mathrm{A}, \mathrm{B}, \mathrm{C}\) are angles f a triangle \(\mathrm{ABC}\). If the lengths of the sides pposite these angles are \(\mathrm{a}, \mathrm{b}, \mathrm{c}\) respectively, then :JEE Mains 2021 Hard
- Let \(Q\) be the mirror image of the point \(P (1,2,1)\) with respect to the plane \(x+2 y+2 z=16\). Let \(T\) be a plane passing through the point \(Q\) and contains the line \(\vec{r}=-\hat{k}+\lambda(\hat{i}+\hat{j}+2 \hat{k}), \lambda \in R\). Then, which of the following points lies on \(T\) ?JEE Mains 2022 Hard
- Let a line passing through the point \((-1,2,3)\) intersect the lines \(L_1: \frac{x-1}{3}=\frac{y-2}{2}=\frac{z+1}{-2}\) at \(\mathrm{M}(\alpha, \beta, \gamma)\) and \(\mathrm{L}_2: \frac{\mathrm{x}+2}{-3}=\frac{\mathrm{y}-2}{-2}=\frac{\mathrm{z}-1}{4}\) at \(\mathrm{N}(\mathrm{a}, \mathrm{b}\), c). Then the value of \(\frac{(\alpha+\beta+\gamma)^2}{(a+b+c)^2}\) equalsJEE Mains 2024 Hard
- An angle between the plane, \(x + y + z = 5\) and the line of intersection of the planes, \(3x + 4y + z- 1 = 0\) and \(5x + 8y + 2z+ 14 = 0\) , isJEE Mains 2018 Hard
- Let the domains of the functions
\(\mathrm{f}(\mathrm{x})=\log _4 \log _3 \log _7\left(8-\log _2\left(\mathrm{x}^2+4 \mathrm{x}+5\right)\right)\) and \(g(x)=\sin ^{-1}\left(\frac{7 x+10}{x-2}\right)\) be \((\alpha, \beta)\) and \([\gamma, \delta]\), respectively. Then \(\alpha^2+\beta^2+\gamma^2+\delta^2\) is equal to :-JEE Mains 2025 Medium - The general solution of the differential equation, \(\sin \,2x\,\left( {\frac{{dy}}{{dx}} - \sqrt {\tan \,x} } \right) - y = 0,\) isJEE Mains 2014 Hard
More PYQs from JEE Mains
- The number of sequences of ten terms, whose terms are either 0 or 1 or 2 , that contain exactly five 1 s and exactly three 2 s , is equal toJEE Mains 2025 Easy
- If the sum of the squares of the reciprocals of the roots \(\alpha\) and \(\beta\) of the equation \(3 x^{2}+\lambda x-1=0\) is 15 , then \(6\left(\alpha^{3}+\beta^{3}\right)^{2}\) is equal toJEE Mains 2022 Hard
- The smallest natural number \(n,\) such that the coefficient of \(x\) in the expansion of \({\left( {{x^2}\, + \,\frac{1}{{{x^3}}}} \right)^n}\) is \(^n{C_{23}}\) isJEE Mains 2019 Hard
- The height of a right circular cylinder of maximum volume inscribed in a sphere of radius \(3\) isJEE Mains 2019 Hard
- The plane through the intersection of the plane \(x + y + z = 1\) and \(2x + 3y + z - 4 = 0\) and parallel to \(y -\) axis also pass through the pointJEE Mains 2019 Hard
- Let O be the origin, and P and Q be two points on the rectangular hyperbola \(xy = 12\) such that the mid point of the line segment PQ is \(\left(\dfrac{1}{2}, -\dfrac{1}{2}\right)\). Then the area of the triangle OPQ equals:JEE Mains 2026 Medium