AP EAMCET · Maths · Trigonometric Ratios & Identities
If \(\cos (A-B)=3 / 5\) and \(\tan A \tan B=2\), then which one of the following is true?
- A \(\sin (A+B)=\frac{1}{5}\)
- B \(\sin (A+B)=-\frac{1}{5}\)
- C \(\cos (A-B)=\frac{1}{5}\)
- D \(\cos (A+B)=-\frac{1}{5}\)
Answer & Solution
Correct Answer
(D) \(\cos (A+B)=-\frac{1}{5}\)
Step-by-step Solution
Detailed explanation
Given, \(\cos (A-B)=\frac{3}{5}\) and \(\tan A \tan B=2\) \(\Rightarrow \quad \frac{\sin A \sin B}{\cos A \cos B}=2\) Using componendo and dividendo…
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 \(A=(2,3,4)\) and \(B=(-2,3,4)\), then the locus of a point \(P\) such that \(\mathrm{PA}+\mathrm{PB}=4\) isAP EAMCET 2023 Hard
- If \(3 \sin x+4 \cos x=5\), then \(6 \tan \frac{x}{2}-9 \tan ^2 \frac{x}{2}\) is equal toAP EAMCET 2012 Easy
- By the definition of the definite integral, the value of
\[
\lim _{n \rightarrow \infty}\left(\frac{1}{\sqrt{n^2-1}}+\frac{1}{\sqrt{n^2-2^2}}+\ldots+\frac{1}{\sqrt{n^2-(n-1)^2}}\right)
\]
is equal toAP EAMCET 2016 Easy - If \(\cos (x-y), \cos x, \cos (x+y)\) are three distinct numbers which are in harmonic progression and \(\cos x \neq \cos y\), then \(1+\cos y\) is equal toAP EAMCET 2010 Medium
- \(\lim _{n \rightarrow \infty}\left[\frac{1^k+2^k+3^k+\ldots+n^k}{n^{k+1}}\right]=\)AP EAMCET 2017 Medium
- If the pair of lines \(2 x^2+3 x y+y^2=0\) makes angles \(\theta_1\) and \(\theta_2\) with the positive direction of the X-axis, then \(\left|\tan \left(\theta_1-\theta_2\right)\right|=\)AP EAMCET 2017 Medium
More PYQs from AP EAMCET
- Let \([\mathrm{t}]\) represents the greatest integer not more than \(\mathrm{t}\).Then the number of discontinuous points of \(f(x)$$=\left[X^{\frac{1}{x}}\right]\)in \((0, \infty)\) isAP EAMCET 2023 Easy
- Identify the reaction/process in which the entropy decreasesAP EAMCET 2022 Easy
- If \(m\) and M denote the mean deviations about mean and about median respectively of the data \(20,5.15,2,7,3,11\) then the mean deviation about the mean of \(m\) and \(M\) isAP EAMCET 2024 Hard
- Find the conjugate of \(\frac{5 i}{7+i}\)AP EAMCET 2020 Easy
- If \(\int \frac{a \cos x+3 \sin x}{5 \cos x+2 \sin x} d x=\frac{26}{29} x-\frac{k}{29} \log |5 \cos x+2 \sin x|+c\), then \(|a+k|=\)AP EAMCET 2025 Medium
- The current in an inductor of self-inductance \(L=40 \mathrm{mH}\) is to be increased uniformly from \(2 \mathrm{~A}\) to \(12 \mathrm{~A}\) in \(8 \mathrm{~ms}\). The emf induced in the inductor during this process isAP EAMCET 2021 Medium