AP EAMCET · Maths · Trigonometric Equations
If \(\tan \mathrm{B}=\frac{2 \sin \mathrm{A} \sin \mathrm{C}}{\sin (\mathrm{A}+\mathrm{C})}\), then \(\tan \mathrm{A}, \tan \mathrm{B}\) and \(\tan \mathrm{C}\) are in
- A Arithmetic progression
- B Harmonic progression
- C Geometric progression
- D Arithmetico - geometric progression
Answer & Solution
Correct Answer
(B) Harmonic progression
Step-by-step Solution
Detailed explanation
\(\tan B=\frac{2 \sin A \sin C}{\sin (A+C)} \Rightarrow \frac{1}{\tan B}=\frac{\sin (A+C)}{2 \sin A \sin C}\) \(\Rightarrow \frac{2}{\tan B}=\frac{1}{\tan C}+\frac{1}{\tan A}\) \(\therefore \quad \tan \mathrm{A}, \tan \mathrm{B} \& \tan \mathrm{C}\) are in harmonic progression.
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 \(\mathbf{a}, \mathbf{b}\) and \(\mathbf{c}\) be non-zero vectors such that \((\mathbf{a} \times \mathbf{b}) \times \mathbf{c}=\frac{1}{3}|\mathbf{b} \| \mathbf{c}| \mathbf{a}\). If \(\theta\) is the acute angle between the vectors \(\mathbf{b}\) and \(\mathbf{c}\), then \(\sin \theta\) is equal toAP EAMCET 2021 Medium
- Number of triangle formed by the lines \(x-y+3=0,2 x-y+3=0,3 x-y+2=0\) and \(x+y-3=0\) isAP EAMCET 2022 Easy
- If \(z=1+i \sqrt{3}\) then \(|\operatorname{Arg} z|+|\operatorname{Arg} \bar{z}|\) is equal toAP EAMCET 2010 Hard
- The coefficient of \(x^4\) in the expansion of \(\left(1-x+x^2-x^3\right)^4\) isAP EAMCET 2016 Medium
- \(\sin 120^{\circ} \cos 150^{\circ}-\cos 240^{\circ} \sin 330^{\circ}\) is equal to :AP EAMCET 2006 Easy
- Assertion (A): \(\int_0^{\frac{\pi}{2}}\left(\sin ^6 x+\cos ^6 x\right) d x\) lies in the interval \(\left(\frac{\pi}{8}, \frac{\pi}{2}\right)\)
Reason (R): \(\sin ^6 x+\cos ^6 x\) is a periodic function with period \(\frac{\pi}{2}\)AP EAMCET 2023 Hard
More PYQs from AP EAMCET
- The product of an amine ' \(\mathrm{X}\) ' with benzene sulphonyl chloride produces the product which is insoluble in alkali. The product of ' \(\mathrm{X}\) ' with ethanoyl chloride isAP EAMCET 2023 Easy
- If \(f(x)=\left\{\begin{array}{lll}x-5, & \text { for } x \leq 1 \\ 4 x^2-9, & \text { for } 1 < x < 2 \\ 3 x+4, & \text { for } x \geq 2,\end{array}\right.\) then \(f^{\prime}\left(2^{+}\right)\)is equal toAP EAMCET 2007 Medium
- If the height of a projectile at a time of 2 s from the beginning of motion is 60 m, then the time of flight of the projectile is (Acceleration due to gravity \(=10 \mathrm{~m} \mathrm{~s}^{-2}\) )AP EAMCET 2025 Medium
- The point \(P(a, b)\) lies on the straight line \(3 x+2 y=13\) and the point \(Q(b, a)\) lies on the straight line \(4 x-y=5\). Then the equation of the line \(P Q\) isAP EAMCET 2017 Medium
- The elevation in the boiling point of aqueous urea solution is \(0.104 \mathrm{~K}\). What is its \(\Delta \mathrm{T}_{\mathrm{f}}\) (in \(\mathrm{K}\) ) value? (for Water \(\mathrm{K}_{\mathrm{b}}=0.52 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}, \mathrm{~K}_{\mathrm{f}}=1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\) )AP EAMCET 2023 Easy
- At 290 K , a vessel (I) contains equal moles of three liquids (A, B, C). The boiling points of A, B and C are 350,373 and 308 K respectively. Vessel (I) is heated to 300 K and vapours were collected into vessel (II). Identify the correct statements. (Assume vessel (I) contains liquids and vapours and vessel (II) contains only vapours)
I. Vessel - I is rich in liquid \(B\)
II. Vessel - II is rich in vapour of C
III. The vapour pressures of A, B, C in Vessel (I) at 290 K follows the order \(\mathrm{C}\gt\mathrm{A}\gt\mathrm{B}\).AP EAMCET 2024 Medium