MHT CET · Maths · Inverse Trigonometric Functions
\(\tan \left(\cos ^{-1} \frac{1}{\sqrt{2}}+\tan ^{-1} \frac{1}{2}\right)=\)
- A 1
- B 2
- C 3
- D 4
Answer & Solution
Correct Answer
(C) 3
Step-by-step Solution
Detailed explanation
\(\tan \left(\cos ^{-1} \frac{1}{\sqrt{2}}+\tan ^{-1} \frac{1}{2}\right)\)
Let \(\theta=\cos ^{-1} \frac{1}{\sqrt{2}}\) and \(\phi=\tan ^{-1} \frac{1}{2}\)
\(\begin{aligned}
& \therefore \quad \cos \theta=\frac{1}{\sqrt{2}} \text { and } \tan \phi=\frac{1}{2} \\
& \therefore \quad \tan \theta=1 \\
& \quad \text { Given expression }=\tan (\theta+\phi) \\
&=\frac{\tan \theta+\tan \phi}{1-\tan \theta \tan \phi} \\
&=\frac{1+\frac{1}{2}}{1-\frac{1}{2}}=3
\end{aligned}\)
Let \(\theta=\cos ^{-1} \frac{1}{\sqrt{2}}\) and \(\phi=\tan ^{-1} \frac{1}{2}\)
\(\begin{aligned}
& \therefore \quad \cos \theta=\frac{1}{\sqrt{2}} \text { and } \tan \phi=\frac{1}{2} \\
& \therefore \quad \tan \theta=1 \\
& \quad \text { Given expression }=\tan (\theta+\phi) \\
&=\frac{\tan \theta+\tan \phi}{1-\tan \theta \tan \phi} \\
&=\frac{1+\frac{1}{2}}{1-\frac{1}{2}}=3
\end{aligned}\)
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
- If one end of the diameter is \((1,1)\) and the other end lies on the line \(x+y=3\), then locus of centre of circle isMHT CET 2008 Medium
- The maximum value of the function \(\frac{\log x}{x}, x \neq 0\) isMHT CET 2020 Medium
- The maximum value of \(z=7 x+8 y\) subject to the constraints \(x+y \leq 20, y \geq 5, x \leq 10, x \geq 0, y \geq 0\) isMHT CET 2023 Medium
- If \(\sin \theta=\frac{1}{2}\left(x+\frac{1}{x}\right)\), then \(\sin 3 \theta+\frac{1}{2}\left(x^3+\frac{1}{x^3}\right)=\)MHT CET 2025 Medium
- The order of the differential equation whose solution is \(a e^{x}+b e^{2 x}+c e^{3 x}+d=0\), isMHT CET 2010 Easy
- If \(\mathrm{G}(3,-5, \mathrm{r})\) is the centroid of \(\triangle \mathrm{ABC}\), where \(\mathrm{A} \equiv(7,-8,1)\), \(B \equiv(p, q, 5), C \equiv(q+1,5 p, 0)\) are vertices of the triangle \(A B C\), then the values of \(p, q, r\) are respectivelyMHT CET 2021 Easy
More PYQs from MHT CET
- Calculate rate constant of a first order reaction having pre exponential factor \(1.6 \times 10^{13} \mathrm{~s}^{-1} \quad\left(\mathrm{E}_{\mathrm{a}} / 2.303 \mathrm{RT}=21\right)\)MHT CET 2025 Medium
- If \(\mathrm{f}(x)\) is a function satisfying \(\mathrm{f}^{\prime}(x)=\mathrm{f}(x)\) with \(\mathrm{f}(0)=1\) and \(\mathrm{g}(x)\) is a function that satisfies \(\mathrm{f}(x)+\mathrm{g}(x)=x^2\). Then the value of the integral \(\int_0^1 \mathrm{f}(x) \mathrm{g}(x) \mathrm{d} x\) isMHT CET 2023 Medium
- Identify the hydrocarbon compound from following containing carbon atoms in the range of \(\mathrm{C}_{6}\) to \(\mathrm{C}_{8}\) ?MHT CET 2020 Easy
- Two charges \(\mathrm{q}_1=+6 \mathrm{q}\) and \(\mathrm{q}_2=-3 \mathrm{q}\) are placed as shown in figure. A proton is placed on x -axis away from \(\mathrm{q}_2\). To remain proton in equilibrium, the distance between \(\mathrm{q}_1\) and proton is
MHT CET 2025 Medium - Two wires \(\mathrm{A}\) and \(\mathrm{B}\) having same length and material are stretched by the same force.
Their diameters are in the ratio \(1: 3\). The ratio of energy density of wire \(A\) to that of wire B when stretched, isMHT CET 2020 Medium - \(\bar{a}=\hat{i}-\hat{\mathrm{j}}, \overline{\mathrm{b}}=\hat{\mathrm{j}}-\hat{\mathrm{k}}, \overline{\mathrm{c}}=\hat{\mathrm{k}}-\hat{i}\) then a unit vector \(\overline{\mathrm{d}}\) such that \(\bar{a} \cdot \bar{d}=0=[\bar{b} \bar{c} \bar{d}]\) isMHT CET 2025 Medium