AP EAMCET · Maths · Trigonometric Ratios & Identities
\(\cos ^2(x)+\cos ^2\left(x+\frac{\pi}{3}\right)+\cos ^2\left(x-\frac{\pi}{3}\right)=\)
- A \(\frac{3}{2}\)
- B \(\frac{1}{2}\)
- C \(\frac{-3}{2}\)
- D \(\frac{-1}{2}\)
Answer & Solution
Correct Answer
(A) \(\frac{3}{2}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \cos ^2 x+\cos ^2\left(x+\frac{\pi}{3}\right)+\cos ^2\left(x-\frac{\pi}{3}\right) \\ & \because \quad \cos 2 x=2 \cos ^2 x-1 \\ & \Rightarrow \quad \cos ^2 x=\frac{\cos 2 x+1}{2} \\ & \Rightarrow \quad\left[\frac{1+\cos 2 x}{2}\right]+\left[\frac{1+\cos \left(2…
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 \(\mathbf{a}, \mathbf{b}\) and \(\mathbf{c}\) be 3 non-coplanar vectors and \((\mathbf{a}-\lambda \mathbf{b}),(\mathbf{b}-2 \mathbf{c}) \times(\mathbf{c}+2 \mathbf{a})=0\), then \(\lambda\) is equal toAP EAMCET 2021 Medium
- If \(I_n=\int \frac{\sin n x}{\cos x} d x\), then \(I_n=\)AP EAMCET 2017 Medium
- \(\int \frac{(1+x) e^x}{\cot \left(x e^x\right)} d x=\)AP EAMCET 2020 Medium
- If \(\bar{a}\) and \(\bar{b}\) are not perpendicular to each other, \(\bar{r} \times \bar{a}=\bar{b} \times \bar{a}\) and \(\bar{r} \cdot \bar{c}=0\) then \(\bar{r}=\)AP EAMCET 2017 Medium
- If \(u(n)=\int_0^{\frac{\pi}{2}}(1+\sin t)^n \sin 2 t d t, n \in N\), then \(u(4)=\)AP EAMCET 2023 Hard
- \(\lim _{x \rightarrow \infty}\left(\frac{2+\sin x}{x^2+3}\right)\) is equal toAP EAMCET 2021 Easy
More PYQs from AP EAMCET
- A Young double slit experimental setup is immersed in water of refractive index It has slit separation and the distance between slits and screen is . If the wavelength of incident light on slits is then the fringe width on screen isAP EAMCET 2019 Medium
- If \(\int_a^b x^3 d x=0\) and \(\int_a^b x^2 d x=\frac{2}{3}\), thenAP EAMCET 2021 Easy
- The tangent drawn at an extremity (in the first quadrant) of latus rectum of the hyperbola \(\frac{x^2}{4}-\frac{y^2}{5}=1\) meets the \(x\)-axis and \(y\)-axis at \(A\) and \(B\) respectively.
If O is the origin, then \((\mathrm{OA})^2-(\mathrm{OB})^2=\)AP EAMCET 2025 Medium - The radius of the first orbit of \(\mathrm{Li}^{2+}\) is \(\mathrm{X} Å\). The radius of the third orbit of \(\mathrm{He}^{+}\)(in \(Å\) ) isAP EAMCET 2022 Medium
- In the determination of the internal resistance of a cell with a potentiometer, the error in the measurement of the balancing length is \(\pm 1 \mathrm{~mm}\). When the cell alone is connected in the circuit, the balancing length is obtained at \(60 \mathrm{~cm}\) and when the cell is shunted with a resistance of \(10 \Omega \pm 2 \%\), the balancing length is obtained at \(50 \mathrm{~cm}\). The error in the determination of the internal resistance of the cell isAP EAMCET 2017 Easy
- The centre of a square of side 4 units length is \((3,7)\) and one of the diagonals is parallel to the line \(y=x\). If \(\left(\mathrm{x}_1, \mathrm{y}_1\right),\left(\mathrm{x}_2, \mathrm{y}_2\right),\left(\mathrm{x}_3, \mathrm{y}_3\right)\) and \(\left(\mathrm{x}_4, \mathrm{y}_4\right)\) are the vertices of this square, then \(\frac{y_1 y_2 y_3 y_4}{x_1 x_2 x_3 x_4}=\)AP EAMCET 2023 Hard