TS EAMCET · Maths · Trigonometric Equations
If \(A+B+C=270^{\circ}\), then \(\cos 2 A+\cos 2 B+\cos 2 C\) is equal to :
- A \(4 \sin A \sin B \sin C\)
- B \(4 \cos A \cos B \cos C\)
- C \(1-4 \sin A \sin B \sin C\)
- D \(1-4 \cos A \cos B \cos C\)
Answer & Solution
Correct Answer
(C) \(1-4 \sin A \sin B \sin C\)
Step-by-step Solution
Detailed explanation
\(\cos 2 A+\cos 2 B+\cos 2 C\) \(=2 \cos (A+B) \cos (A-B)+1-2 \sin ^2 C\) \(=2 \cos \left(\frac{3 \pi}{2}-C\right) \cos (A-B)+1-2 \sin ^2 C\) \(\left[\because A+B+C=270^{\circ} \Rightarrow B+C=\frac{3 \pi}{2}-C\right\rfloor\) \(=1-2 \sin C[\cos (A-B)+\sin C]\)…
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
- The area (in square unit) of the triangle formed by \(x+y+1=0\) and the pair of straight lines \(x^2-3 x y+2 y^2=0\) isTS EAMCET 2009 Medium
- If \(A=\left[\begin{array}{lll}9 & 3 & 0 \\ 1 & 5 & 8 \\ 7 & 6 & 2\end{array}\right]\) and \(\mathrm{AA}^T-\mathrm{A}^2=\left[\begin{array}{lll}a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{array}\right]\), then \(\sum_{\substack{1 \leq i \leq 3 \\ 1 \leq j \leq 3}} a_{i j}=\)TS EAMCET 2024 Medium
- \(\int_0^{\pi / 2} \frac{d x}{4+5 \sin x}\)TS EAMCET 2020 Hard
- Let \(\mathbf{a}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-3 \hat{\mathbf{k}}\) and \(\mathbf{b}=\hat{\mathbf{i}}+3 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}\). Then the volume of the parallelopiped having coterminous edges as \(\mathbf{a}, \mathbf{b}\) and \(\mathbf{c}\), where \(\mathrm{c}\) is the vector perpendicular to the plane of \(\mathbf{a}, \mathbf{b}\) and \(|c|=2\) isTS EAMCET 2017 Medium
- If the probability distribution of a random variable \(X\) is as follows, then the variance of \(X\) is \begin{array}{|l|c|c|c|c|}\hlineX=x & 2 & 3 & 5 & 9 \\hlineP(X=x) & k & 2 k & 3 k^2 & k^2 \\hline\end{array}TS EAMCET 2024 Easy
- The direction cosines of the normal to the plane containing the lines having direction ratios \(1,2,1\) and \(4,5,-3\) areTS EAMCET 2020 Easy
More PYQs from TS EAMCET
- The incorrect statement about Castner-Kellner cell process isTS EAMCET 2025 Easy
- If the energy gap of a semiconductor used for the fabrication of an LED is nearly 1.9 eV, then the color of the light emitted by the LED isTS EAMCET 2025 Easy
- The area (in square units) bounded by the curves \(|x|=2,|y|=2\) and \(x y \leq \frac{1}{2}\) isTS EAMCET 2020 Easy
- Let \(\Pi\) be a plane containing the points \((0,-5,-1),(1,-2,5),(-3,5,0)\) and \(L\) be a line passing through the point \((0,-5,-1)\) and parallel to the vector \(\hat{\mathbf{i}}+5 \hat{\mathbf{j}}-6 \hat{\mathbf{k}}\). Then the length of the projection of the unit normal vector to the plane \(\Pi\) on the line \(L\) isTS EAMCET 2020 Medium
- are non-coplanar vectors. If the position vector of the point of intersection of the line and the plane is thenTS EAMCET 2021 Medium
- The Cartesian equation of a plane parallel to the plane and at a distance of units from it isTS EAMCET 2021 Easy