WBJEE · Maths · Inverse Trigonometric Functions
A positive acute angle is divided into two parts whose tangents are \(\frac{1}{2}\) and \(\frac{1}{3}\). Then the angle is
- A \(\pi / 4\)
- B \(\pi / 5\)
- C \(\pi / 3\)
- D \(\pi / 6\)
Answer & Solution
Correct Answer
(A) \(\pi / 4\)
Step-by-step Solution
Detailed explanation
Hints : Angle \(\theta=\tan ^{-1} \frac{1}{2}+\tan ^{-1} \frac{1}{3}=\tan ^{-1}\left(\frac{\frac{1}{2}+\frac{1}{3}}{1-\frac{1}{2} \cdot \frac{1}{3}}\right)\) \(=\tan ^{-1}\left(\frac{5 / 6}{5 / 6}\right)=\tan ^{-1}(1)=\pi / 4\)
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
- If \(\mathrm{A}\) and \(\mathrm{B}\) are two matrices such that \(\mathrm{A}+\mathrm{B}\) and \(\mathrm{AB}\) are both defined, thenWBJEE 2011 Easy
- The value of \(\lambda\) such that the system of equations \(2x-y-2 y=2 ; x-2 y+z=-4\),\(x+y+\lambda z=4,\) has no solution, isWBJEE 2015 Easy
- Let \(f(x)>0\) for all \(x\) and \(f^{\prime}(x)\) exists for all \(x\). If \(f\) is the inverse function of \(h\) and \(h^{\prime}(x)=\frac{1}{1+\log x} \cdot\) Then, \(f^{\prime}(x)\) will beWBJEE 2019 Medium
- An urn contains 8 red and 5 white balls. Three balls are drawn at random. Then, the probability that balls of both colours are drawn isWBJEE 2012 Easy
- If \(z_1\) and \(z_2\) be two roots of the equation \(z^2+a z+b=0, a^2 \lt 4 b\), then the origin, \(z_1\) and \(z_2\) form an equilateral triangle ifWBJEE 2024 Hard
- A line through the point \(\mathrm{A}(2,0)\) which makes an angle of \(30^{\circ}\) with the positive direction of \(x\)-axis is rotated about A in clockwise direction through an angle \(15^{\circ}\). Then the equation of the straight line in the new position isWBJEE 2009 Easy
More PYQs from WBJEE
- For \(-\frac{\pi}{2} < x < \frac{3 \pi}{2}, \quad\) the \(\quad\) value \(\quad\) of \(\frac{d}{d x}\left\{\tan ^{-1} \frac{\cos x}{1+\sin x}\right\}\) is equal toWBJEE 2012 Medium
- Let \(f: R \rightarrow R\) be a twice continuously differentiable function such that \(f(0)=f(1)=f^{\prime}(0)=0 .\) ThenWBJEE 2018 Easy
- A metal sphere of radius \(R\) carrying charge \(q\) is surrounded by a thick concentric metal shell of inner and outer radii a and \(\mathrm{b}\) respectively. The net charge on the shell is zero. The potential at the centre of the sphere, when the outer surface of the shell is grounded will beWBJEE 2021 Medium
- \(\mathrm{A}=\{1,2,3,4\}, \mathrm{B}=\{1,2,3,4,5,6\}\) are two sets, and function \(\mathrm{f}: \mathrm{A} \rightarrow \mathrm{B}\) is defined by \(\mathrm{f}(\mathrm{x})=\mathrm{x}+2 \forall \mathrm{x} \in \mathrm{A}\), then the function \(\mathrm{f}\) isWBJEE 2010 Easy
- Let \(f\) and \(g\) be periodic functions with the periods \(T_{1}\) and \(T_{2}\) respectively. Then \(f+g\) isWBJEE 2021 Easy
- For what values of \(\mathrm{x}\), the function \(\mathrm{f}(\mathrm{x})=\mathrm{x}^4-4 \mathrm{x}^3+4 \mathrm{x}^2+40\) is monotone decreasing?WBJEE 2010 Easy