COMEDK · Maths · 8. Trigonometric Ratios & Identities
If \(\sin A + \sin 2A = x\) and \(\cos A + \cos 2A = y\) then the value of the expression \((x^2 + y^2)(x^2 + y^2 - 3)\) equals
- A \(3y\)
- B \(2y\)
- C \(\dfrac{y}{2}\)
- D \(0\)
Answer & Solution
Correct Answer
(B) \(2y\)
Step-by-step Solution
Detailed explanation
Given equations are: \(x = \sin A + \sin 2A\) \(y = \cos A + \cos 2A\) Squaring and adding both equations, we get: \(x^2 + y^2 = (\sin A + \sin 2A)^2 + (\cos A + \cos 2A)^2\) \(x^2 + y^2 = (\sin^2 A + \cos^2 A) + (\sin^2 2A + \cos^2 2A) + 2(\sin A \sin 2A + \cos A \cos 2A)\)…
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
- A line makes the same angle \(\theta\) with each of the \(x\) and \(z\)-axes. If the angle \(\beta\), which it makes with the \(y\)-axis is such that \(\sin ^2 \beta=3 \sin ^2 \theta\), then \(\cos ^2 \theta\) equalsCOMEDK 2024 Medium
- If the circles \(x^{2}+y^{2}+2 g x+2 f y=0\) and \(x^{2}+y^{2}+2 g^{\prime} x+2 f^{\prime} y=0\) touch each other, thenCOMEDK 2018 Medium
- \(f(x)=\left(\frac{5}{x}+7\right)\), where \(x \neq 0\) is decreasing forCOMEDK 2017 Easy
- \(\text { The value of } \dfrac{i^{1004}+i^{1006}+i^{1008}+i^{1010}+i^{1012}}{i^{510}+i^{508}+i^{506}+i^{504}+i^{502}} \text { is }\)COMEDK 2024 Easy
- If matrix \(A=\left[\begin{array}{cc}2 & -2 \\ -2 & 2\end{array}\right]\) and \(A^{2}=p A\), then the value of \(p\) isCOMEDK 2021 Medium
- The length of \(y\)-intercept of the circle \(x^2+y^2-6 x+4 y+3=0\) isCOMEDK 2024 Easy
More PYQs from COMEDK
- A photon emitted during the de-excitation of electron from a state \(\mathrm{n}\) to the second excited state in a hydrogen atom, irradiates a metallic electrode of work function \(0.5 \mathrm{~eV}\), in a photocell, with a stopping voltage of \(0.47 \mathrm{~V}\). Obtain the value of quantum number of the state '\(n\)'.COMEDK 2024 Medium
- A cell of emf \(2 \mathrm{~V}\) is connected with a load of resistance \(1.5 \Omega\). The power delivered by the cell to the load is maximum, then power transferred to the load isCOMEDK 2022 Easy
- When \(50 \mathrm{~cm}^{3}\) of \(0.2 \mathrm{NH}_{2} \mathrm{SO}_{4}\) is mixed with \(50 \mathrm{~cm}^{3}\) of \(1 \mathrm{~N} \mathrm{KOH}\), the heat liberated isCOMEDK 2016 Easy
- For a cell \(2 \mathrm{M}_{(\mathrm{S})}+\mathrm{O}_2(\mathrm{~g})+4 \mathrm{H}^{+} \rightarrow 2 \mathrm{M}^{2+}(\mathrm{aq})+2 \mathrm{H}_2 \mathrm{O}_{(\mathrm{l})}\) the \(\mathrm{E}^0\) cell \(=+1.67 \mathrm{~V}\). When \(\left[\mathrm{M}^{2+}\right]\) is \(1.0 \times 10^{-3} \mathrm{M}\) and \(\mathrm{p}\left(\mathrm{O}_2\right)\) is 0.1 atm , the EMF of the cell becomes +1.57 V . Calculate the pH of the electrochemical cell.COMEDK 2025 Medium
- If a straight line passing through a fixed point \((a, b)\), where \(a, b > 0\), makes positive intercepts OA and OB on the coordinate axes, then the least value of OA + OB is:COMEDK 2026 Medium
- An AC voltage source of variable angular frequency \(\omega\) and fixed amplitude \(\mathrm{V}_0\) is connected in series with a capacitance \(\mathrm{C}\) and an electric bulb of resistance \(\mathrm{R}\) (inductance zero). When \(\omega\) is decreasedCOMEDK 2024 Medium