AP EAMCET · Maths · Trigonometric Ratios & Identities
If \(\sin A+\sin B=\frac{1}{2}\) and \(\cos A+\cos B=1\), then \(\sin \left(\frac{A-B}{2}\right)\) equals
- A \(\pm \frac{\sqrt{13}}{4}\)
- B \(\pm \frac{\sqrt{11}}{4}\)
- C \(\pm \frac{\sqrt{7}}{4}\)
- D \(\pm \frac{\sqrt{17}}{4}\)
Answer & Solution
Correct Answer
(B) \(\pm \frac{\sqrt{11}}{4}\)
Step-by-step Solution
Detailed explanation
Given \(\sin A+\sin B=\frac{1}{2}\) and \(\cos A+\cos B=1\), on square and add the given relations, we get \[ \begin{array}{ll} 2+2(\cos A \cos B+\sin A \sin B)=\frac{1}{4}+1 \\ \Rightarrow & 2 \cos (A-B)=-\frac{3}{4} \\ \Rightarrow & \cos (A-B)=-\frac{3}{8} \end{array} \]…
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 \(I_n=\int_0^{\pi / 4} \tan ^n x d x\), then \(I_2+I_4, I_3+I_5, I_4+I_6, \ldots\), are inAP EAMCET 2010 Hard
- If \(\frac{d y}{d x}=f(x, y)\) is a homogeneous differential equation, then the general form of \(f(x, y)\) isAP EAMCET 2023 Easy
- If the amplitude of \(z-2-3 i\) is \(\frac{\pi}{4}\), then the locus of \(z=x+i y\) is :AP EAMCET 2003 Medium
- If the inverse of \(\left[\begin{array}{ccc}-x & 14 x & 7 x \\ 0 & 1 & 0 \\ x & -4 x & -2 x\end{array}\right]\) is \(\left[\begin{array}{ccc}2 & 0 & 7 \\ 0 & 1 & 0 \\ 1 & -2 & 1\end{array}\right]\), then \(\left|\begin{array}{ccc}x & x+1 & x+2 \\ x+1 & x+2 & x+3 \\ x+2 & x+3 & x+4\end{array}\right|=\)AP EAMCET 2025 Medium
- If and then is equal toAP EAMCET 2021 Medium
- Let \(x_1, x_2, \ldots, x_{11}\) be the observations satisfying \(\sum_{i=1}^{11}\left(x_i-4\right)=22\) and \(\sum_{i=1}^{11}\left(x_i-4\right)^2=154\). If the mean and variance of the observations are \(\alpha\) and \(\beta\), then the quadratic equation having the roots \(\frac{\alpha}{\beta}\) and \(\frac{\beta}{\alpha}\) isAP EAMCET 2025 Medium
More PYQs from AP EAMCET
- If \(\left(\frac{\sin 3 \theta}{\sin \theta}\right)^2-\left(\frac{\cos 3 \theta}{\cos \theta}\right)^2=a \cos b \theta\), then \(a: b=\)AP EAMCET 2025 Medium
- \(\cos ^4 \frac{\pi}{24}-\sin ^4 \frac{\pi}{24}=\)AP EAMCET 2022 Medium
- If the tangent to the curve \(2 y^3=a x^2+x^3\) at the point \((a, a)\) cuts off intercepts \(\alpha\) and \(\beta\) on the coordinate axes, where \(\alpha^2+\beta^2=61\), then the value of \(|a|\) isAP EAMCET 2021 Medium
- In the figure shown, the blocks have equal masses. Friction, mass of the string and the mass of the pulley are negligible. The magnitude of the acceleration of the centre of mass of the two blocks is (Acceleration due to gravity \(=g\)).
AP EAMCET 2019 Medium - If \(x\) is a real number, then the number of solutions of
\(\operatorname{Tan}^{-1}(\sqrt{x(x+1)})+\operatorname{Sin}^{-1}\left(\sqrt{x^2+x+1}\right)=\frac{\pi}{2} \text { is }\)AP EAMCET 2025 Medium - Water is falling on the blades of a turbine from a height of of water pours on the blade per minute. If the whole of energy is transferred to the turbine, power delivered is:AP EAMCET 2021 Medium