JEE Mains · Maths · STD 12 - 2. inverse trigonometric function
If \(\frac{\pi}{2} \leq x \leq \frac{3 \pi}{4}\), then \(\cos ^{-1}\left(\frac{12}{13} \cos x+\frac{5}{13} \sin x\right)\) is equal to
- A \(x-\tan ^{-1} \frac{4}{3}\)
- B \(x+\tan ^{-1} \frac{4}{5}\)
- C \(x-\tan ^{-1} \frac{5}{12}\)
- D \(x+\tan ^{-1} \frac{5}{12}\)
Answer & Solution
Correct Answer
(C) \(x-\tan ^{-1} \frac{5}{12}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \frac{12}{13} \cos x+\frac{5}{13} \sin x \\ & \text { Let } \tan \alpha=\frac{5}{12}, \alpha \in\left(0, \frac{\pi}{2}\right) \\ & \Rightarrow \sin \alpha=\frac{5}{13}, \cos \alpha=\frac{12}{13}\end{aligned}\)…
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 \(y = y(x)\) be the solution curve of the differential equation \((1 + \sin x)\dfrac{dy}{dx} + (y+1)\cos x = 0\), \(y(0) = 0\). If the curve \(y = y(x)\) passes through the point \(\left(\alpha, \dfrac{-1}{2}\right)\), then a value of \(\alpha\) is :JEE Mains 2026 Easy
- The area of the region, inside the circle \((x-2 \sqrt{3})^2+y^2=12\) and outside the parabola \(y^2=2 \sqrt{3} x\) is :JEE Mains 2025 Medium
- Let a triangle be bounded by the lines \(L _{1}: 2 x +5 y =10\); \(L _{2}:-4 x +3 y =12\) and the line \(L _{3}\), which passes through the point \(P (2,3)\), intersect \(L _{2}\) at \(A\) and \(L _{1}\) at \(B\). If the point \(P\) divides the line-segment \(A B\), internally in the ratio \(1: 3\), then the area of the triangle is equal toJEE Mains 2022 Hard
- Let the number of elements in sets \(A\) and \(B\) be five and two respectively. Then the number of subsets of \(A \times B\) each having at least \(3\) and at most \(6\) element is :JEE Mains 2023 Hard
- If \(\alpha \), \(\beta \) and \(\gamma \) are three consecutive terms of a non-constant \(G.P.\) such that the equations \(\alpha x^2 + 2\beta x + \gamma = 0\) and \(x^2 + x -1 = 0\) have a common root, then \(\alpha(\beta + \gamma )\) is equal toJEE Mains 2019 Hard
- Let \(f\) be a continuous function satisfying \(\int \limits_0^{t^2}\left( f ( x )+ x ^2\right) dx =\frac{4}{3} t ^3, \forall t > 0 . \quad\) Then \(f \left(\frac{\pi^2}{4}\right)\) equal to :JEE Mains 2023 Hard
More PYQs from JEE Mains
- Let a function \(f: R \rightarrow R\) be defined as \(f(x)=\sin x-e^{x} \,\,\,\, \text { if } x \leq 0\) \(\quad\quad\quad a+[-x] \,\,\,\, \text { if } 0\,<\,x\,<\,1\) \(\quad\quad\quad 2 x-b \,\,\,\,\,\,\,\, \text { if } \geq 1\) where \([\mathrm{x}]\) is the greatest integer less than or equal to \(\mathrm{x}\). If \(\mathrm{f}\) is continuous on \(\mathrm{R}\), then \((\mathrm{a}+\mathrm{b})\) is equal to:JEE Mains 2021 Hard
- Let \(A\) and \(B\) be two sets containing four and two elements respectively. Then the number of subsets of the set \(A \times B,\) each having at least three elements is :JEE Mains 2015 Hard
- If \(\int_{0}^{\sqrt{3}} \frac{15 x^{3}}{\sqrt{1+x^{2}+\sqrt{\left(1+x^{2}\right)^{3}}}} d x=\alpha \sqrt{2}+\beta \sqrt{3}\), where \(\alpha, \beta\) are integers, then \(\alpha+\beta\) is equal to.JEE Mains 2022 Hard
- The equation of the plane passing through the line of intersection of the planes \(\vec{r} .(\hat{i}+\hat{j}+\hat{k})=1\) and \(\vec{r} \cdot(2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-\hat{\mathrm{k}})+4=0\) and parallel to the \(\mathrm{x}\)-axis is:JEE Mains 2021 Medium
- Let a line \(L\) pass through the point \(P (2,3,1)\) and be parallel to the line \(x+3 y-2 z-2=0=x-y+2 z\). If the distance of \(L\) from the point \((5,3,8)\) is \(\alpha\), then \(3 \alpha^2\) is equal to \(......\).JEE Mains 2023 Hard
- Let \(f\) be a differentiable function such that \(2(x+2)^2 f(x)-3(x+2)^2=10 \int_0^x(t+2) f(t) d t, x \geq 0\). Then \(f(2)\) is equal to ______.JEE Mains 2025 Hard