JEE Mains · Maths · STD 12 - 2. inverse trigonometric function
Considering the principal values of the inverse trigonometric functions, \(\sin ^{-1}\left(\frac{\sqrt{3}}{2} x+\frac{1}{2} \sqrt{1-x^2}\right),-\frac{1}{2} \lt x \lt \frac{1}{\sqrt{2}}\), is equal to
- A \(\frac{\pi}{4}+\sin ^{-1} x\)
- B \(\frac{\pi}{6}+\sin ^{-1} x\)
- C \(\frac{-5 \pi}{6}-\sin ^{-1} x\)
- D \(\frac{5 \pi}{6}-\sin ^{-1} x\)
Answer & Solution
Correct Answer
(B) \(\frac{\pi}{6}+\sin ^{-1} x\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \sin ^{-1}\left(\frac{\sqrt{3}}{2} x+\frac{1}{2} \sqrt{1-x^2}\right), \frac{-1}{2} \lt x \lt \frac{1}{\sqrt{2}} \\ & \Rightarrow \text { Let } \sin ^{-1}(x)=\theta \quad \frac{-\pi}{6} \lt \theta \lt \frac{\pi}{4} \\ & \Rightarrow x=\sin \theta, \text { then }…
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
- For a differentiable function \(\mathrm{f}: I R \rightarrow I R\), suppose \(f^{\prime}(\mathrm{x})=3 f(\mathrm{x})+\alpha\), where \(\alpha \in \operatorname{IR}, f(0)=1\) and \(\lim _{x \rightarrow-\infty} f(x)=7\). Then \(9 \mathrm{f}\left(-\log _{\mathrm{e}} 3\right)\) is equal to ............JEE Mains 2024 Hard
- Let \(\vec{a}=a_i \hat{i}+a_2 \hat{j}+a_3 \hat{k}\) and \(\vec{b}=b_1 \hat{i}+b_2 \hat{j}+b_3 \hat{k}\) be two vectors such that \(|\vec{a}|=1 ; \quad \vec{a} \cdot \vec{b}=2\) and \(|\vec{b}|=4\). If \(\vec{c}=2(\vec{a} \times \vec{b})-3 \vec{b}\), then the angle between \(\vec{b}\) and \(\vec{c}\) is equal to :JEE Mains 2024 Hard
- The total number of four digit numbers such that each of the first three digits is divisible by the last digit, is equal toJEE Mains 2022 Medium
- Let \(\left(1+x+2 x^{2}\right)^{20}=a_{0}+a_{1} x+a_{2} x^{2}+\ldots+a_{40} x^{40}\) then \(a _{1}+ a _{3}+ a _{5}+\ldots+ a _{37}\) is equal toJEE Mains 2021 Hard
- \(\lim _{n \rightarrow \infty} \frac{3}{n}\left\{4+\left(2+\frac{1}{n}\right)^2+\left(2+\frac{2}{n}\right)^2+\ldots+\left(3-\frac{1}{n}\right)^2\right\}\) is equal toJEE Mains 2023 Hard
- Let \(z_1\) and \(z_2\) be two complex number such that \(z_1\) \(+z_2=5\) and \(z_1^3+z_2^3=20+15 i\). Then \(\left|z_1^4+z_2^4\right|\) equals-JEE Mains 2024 Hard
More PYQs from JEE Mains
- Let \(A(a, b), B(3,4)\) and \((-6,-8)\) respectively denote the centroid, circumcentre and orthocentre of a triangle. Then, the distance of the point \(P(2 a+3,7 b+5)\) from the line \(2 x+3 y-4=0\) measured parallel to the line \(x-2 y-1=0\) isJEE Mains 2024 Hard
- If the angles of elevation of the top of a tower from threecollinear points \(A, B\) and \(C\) on a line leading to the foot of the tower are \(30^o , 45^o \) and \(60^o \) respectively, then the ratio \(AB : BC\) is:JEE Mains 2015 Hard
- \(\mathop {{\rm{lim}}}\limits_{x \to 0} \frac{{\left( {1 - cos2x} \right)\left( {3 + \cos x} \right)}}{{x\;tan4x}}\) =JEE Mains 2015 Medium
- The shortest distance between the lines \(\frac{x-3}{3}=\frac{y-8}{-1}=\frac{z-3}{1}\) and \(\frac{x+3}{-3}=\frac{y+7}{2}=\frac{z-6}{4}\) isJEE Mains 2020 Medium
- The maximum value of the term independent of \('t'\) in the expansion of \(\left( tx ^{\frac{1}{5}}+\frac{(1- x )^{\frac{1}{10}}}{ t }\right)^{10}\) where \(x \in(0,1)\) isJEE Mains 2021 Hard
- For \(\alpha \in N\), consider a relation \(R\) on \(N\) given by \(R =\{( x , y ): 3 x +\alpha y\) is a multiple of 7\(\}\).The relation \(R\) is an equivalence relation if and only if.JEE Mains 2022 Medium