AP EAMCET · Maths · Trigonometric Equations

$\sum_{k=1}^3 \cos ^2\left((2 k-1) \frac{\pi}{12}\right)$ is equal to

A $0$
B $\frac{1}{2}$
C $-\frac{1}{2}$
D $\frac{3}{4}$

Verified Solution

Answer & Solution

Correct Answer

(D) $\frac{3}{4}$

Step-by-step Solution

Detailed explanation

We have…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

The probability distribution of a discrete random variable X is given below
X = x -1 0 1 2
P(X = x) $\frac{1}{3}$ $\frac{1}{6}$ $\frac{1}{6}$ $\frac{1}{3}$

Then the value of $6 \Sigma\left(\mathrm{x}^2\right) \mathrm{P}(\mathrm{X}=\mathrm{x})-\operatorname{var}(\mathrm{X})=$

AP EAMCET 2025 Medium
If $g(x)=\frac{x}{[x]}$ for $\mathrm{x}>2$, then $\lim _{x \rightarrow 2} \frac{g(x)-g(2)}{x-2}$ is equal to

AP EAMCET 2015 Easy
If ${ }^{(n-1)} C_3+{ }^{(n-1)} C_4>{ }^n C_3$, then the minimum value of $n$ is

AP EAMCET 2011 Easy
Let $\mathrm{P}(\mathrm{h}, \mathrm{k})$ be the point of contact of the tangent to the hyperbola $5 x^2-7 y^2-35=0$ which is parallel to the line $\sqrt{2} x-y+\lambda=0$. If $P$ lies in the third quadrant then $3 h^2-2 k=$

AP EAMCET 2023 Medium
The solution of $\frac{d y}{d x}=\left(\frac{x}{y}\right)^{-1 / 3}$ is

AP EAMCET 2002 Medium
The shortest distance between the skew lines $\vec{r}(-\hat{i}-2 \hat{j}-3 \hat{k})+t(3 \hat{i}-2 \hat{j}-2 \hat{k})$ and $\vec{r}=(7 \hat{i}+4 \hat{k})+s(\hat{i}-2 \hat{j}+2 \hat{k})$ is

AP EAMCET 2024 Easy

X = x	-1	0	1	2
P(X = x)	\(\frac{1}{3}\)	\(\frac{1}{6}\)	\(\frac{1}{6}\)	\(\frac{1}{3}\)

Explore more questions on app

From AP EAMCET

$\cot \left(\sum_{n=1}^{50} \tan ^{-1}\left(\frac{1}{1+n+n^2}\right)\right)=$

AP EAMCET 2024 Medium
A box contains 30 toys of same size in which 10 toys are white and all the remaining toys are blue. A toy is drawn at random from the box and it is replaced in the box after noting down its colour. If 5 toys are drawn in this way, then the probability of getting atmost 2 white toys is

AP EAMCET 2019 Hard
In H is orthocentre of $\triangle \mathrm{ABC}$ and $\mathrm{AH}=x ; \mathrm{BH}=y ; \mathrm{CH}=$ $z$ then $\frac{a b c}{x y z}=$

AP EAMCET 2024 Hard
The radius of the circle having $3 x-4 y+4=0$ and $6 x-8 y-7=0$ as its tangents is

AP EAMCET 2022 Medium
Let $A$ and $B$ be events with $P(A)=\frac{1}{3}, P(B)=\frac{1}{4}$ and $P(A \cup B)=\frac{1}{2}$. Then which of the following statement is incorrect?

AP EAMCET 2021 Easy
$\int \frac{1 + \tan x \tan (x + a)}{\tan x \tan (x + a)} d x =$

AP EAMCET 2022 Hard

Explore more questions on app

\(\sum_{k=1}^3 \cos ^2\left((2 k-1) \frac{\pi}{12}\right)\) is equal to

Answer & Solution

Step-by-step Solution

See the Complete Solution