AP EAMCET · Maths · Trigonometric Ratios & Identities
If \(\sin \theta+\cos \theta=p\) and \(\sin ^3 \theta+\cos ^3 \theta=q\), then \(p\left(p^2-3\right)\) is equal to
- A \(q\)
- B \(2 q\)
- C \(-q\)
- D \(-2 q\)
Answer & Solution
Correct Answer
(D) \(-2 q\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { Given, } \quad \sin \theta+\cos \theta=p \\ & \text { and } \quad \sin ^3 \theta+\cos ^3 \theta=q \\ & \Rightarrow \quad(\sin \theta+\cos \theta) \\ & \quad\left(\sin ^2 \theta-\sin \theta \cdot \cos \theta+\cos ^2 \theta\right)=q\end{aligned}\)…
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 four dice are thrown simultaneously, then the probability that none of the dice shows the number 1 on its face, isAP EAMCET 2023 Easy
- Let \(\bar{u}, \bar{v}, \bar{w}\) be vectors such that \(|\bar{u}|=1,|\bar{v}|=2,|\bar{w}|=3\). If the projection of \(\bar{v}\) on \(\bar{u}\) is equal to that of \(\bar{w}\) on \(\bar{u}\), and the vectors \(\bar{v}, \bar{w}\) are perpendicular to each other, then \(|\bar{u}-\bar{v}+\bar{w}|=\)AP EAMCET 2017 Hard
- If the equation \(x^4+a x^3+b x^2+c x+d=0\) has three equal roots, then that root isAP EAMCET 2023 Easy
- If \(\log (x+y)-2 x y=0\), then \(y^{\prime}(0)=\)AP EAMCET 2020 Easy
- If \(\mathrm{A}(-3,3), \mathrm{B}(1,1), \mathrm{C}(1,-1)\) and \(\mathrm{D}(-2,-2)\) are the vertices of a quadrilateral, the angle between the diagonals \(\mathrm{AC}\) and \(\mathrm{BD}\) isAP EAMCET 2022 Easy
- Suppose is an isosceles triangle with and . Then the centroid of the triangle isAP EAMCET 2022 Medium
More PYQs from AP EAMCET
- Let \(\mathrm{x} \in \mathbf{R}\) and \(|\mathrm{x}| < 1\). Then \(\tanh ^{-1} x=\)AP EAMCET 2022 Medium
- In the given circuit, when \(A=1, B=1\) the values of \(X\) and Y respectively are
AP EAMCET 2023 Easy - The correct order of decomposition temperature of \(\mathrm{MgCO}_3\) \((\mathrm{X}) . \mathrm{BaCO}_3(\mathrm{Y}), \mathrm{CaCO}_3(\mathrm{Z})\) isAP EAMCET 2024 Easy
- The approximate value of \(\int_1^3 \frac{d x}{2+3 x}\) using Simpson's rule and dividing the interval \([1,3]\) into two equal parts isAP EAMCET 2013 Hard
- The unit vectors orthogonal to \(3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+6 \hat{\mathbf{k}}\) and coplanar with \(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}\) areAP EAMCET 2020 Medium
- Choose the correct option regarding: Assertion Energy of the orbital decreases with increase of ' \(n\) '.
Reason Energy is required in shifting away the negatively charged electron from positively charged nucleusAP EAMCET 2020 Easy