MHT CET · Maths · Trigonometric Equations
If \(\frac{1-\tan \theta}{1+\tan \theta}=\frac{1}{\sqrt{3}}\), where \(\theta \in\left(0, \frac{\pi}{2}\right)\), then \(\theta=\)
- A \(\frac{\pi}{12}\)
- B \(\frac{\pi}{4}\)
- C \(\frac{\pi}{6}\)
- D \(\frac{\pi}{3}\)
Answer & Solution
Correct Answer
(A) \(\frac{\pi}{12}\)
Step-by-step Solution
Detailed explanation
Given \(\frac{1-\tan \theta}{1+\tan \theta}=\frac{1}{\sqrt{3}}\)
\(\therefore \tan \left(\frac{\pi}{4}-\theta\right)=\frac{1}{\sqrt{3}}\)
Comparing with \(\tan \frac{\pi}{6}=\frac{1}{\sqrt{3}}\), we write
\(\frac{\pi}{4}-\theta=\frac{\pi}{6} \)
\( \therefore \theta=\frac{\pi}{4}-\frac{\pi}{6}=\frac{\pi}{12}\)
\(\therefore \tan \left(\frac{\pi}{4}-\theta\right)=\frac{1}{\sqrt{3}}\)
Comparing with \(\tan \frac{\pi}{6}=\frac{1}{\sqrt{3}}\), we write
\(\frac{\pi}{4}-\theta=\frac{\pi}{6} \)
\( \therefore \theta=\frac{\pi}{4}-\frac{\pi}{6}=\frac{\pi}{12}\)
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
- \(\int \frac{d x}{\sqrt{(x-1)(x-2)}}=\)MHT CET 2020 Hard
- \(\int_{1}^{28} \frac{\mathrm{d} x}{x(1+\log x)^{2}}=\)MHT CET 2020 Easy
- Let \(\mathrm{f}\) be a differentiable function such that \(\mathrm{f}(1)=2\) and \(\mathrm{f}^{\prime}(x)=\mathrm{f}(x)\), for all \(x \in \mathrm{R}\). If \(\mathrm{h}(x)=\mathrm{f}(\mathrm{f}(x))\), then \(\mathrm{h}^{\prime}(1)\) is equal toMHT CET 2023 Hard
- If the truth value of the expression \([(p \vee q) \wedge(q \rightarrow r) \wedge(\sim r)] \rightarrow(p \wedge q)\) is False then truth values of \(p, q, r\) are respectively.MHT CET 2025 Medium
- \(\int \mathrm{e}^x\left(\frac{x+5}{(x+6)^2}\right) \mathrm{d} x\) isMHT CET 2025 Medium
- If \(f: \mathrm{R} \rightarrow \mathrm{R}, \mathrm{g}: \mathrm{R} \rightarrow \mathrm{R}\) are two functions defined by \(f(x)=2 x-3, \mathrm{~g}(x)=x^{3}+5\)
then \((\operatorname{fog})^{-1}(x)=\)MHT CET 2020 Hard
More PYQs from MHT CET
- The particular solution of \(\log \left(\frac{d y}{d x}\right)=3 x+4 y\) at \(x=y=0\) isMHT CET 2022 Easy
- A weak monobasic acid dissociates to \(0.001 \%\) in its \(0.01 \mathrm{M}\) solution. What is its dissociation constant?MHT CET 2022 Easy
- In an ionic solid equal number of cations and anions are missing from their regular positions in the crystal lattice creating vacancies is called-MHT CET 2024 Easy
- The ratio of wavelengths for transition of electrons from \(2^{\text {nd }}\) orbit to \(1^{\text {st }}\) orbit of Helium \(\left(\mathrm{He}^{++}\right)\)and Lithium \(\left(\mathrm{Li}^{++}\right)\)is (Atomic number of Helium \(=2\), Atomic number of Lithium = 3)MHT CET 2023 Easy
- Recessive gene present on non homologous part of only one X chromosome of humans will _________ .MHT CET 2023 Easy
- Two uniform wires of same material are vibrating under the same tension. If the first overtone of first wire is equal to the \(2^{\text {nd }}\) overtone of \(2^{\text {nd }}\) wire and radius of the first wire is twice the radius of the \(2^{\text {nd }}\) wire then the ratio of length of first wire to \(2^{\text {nd }}\) wire isMHT CET 2023 Hard