TS EAMCET · Maths · Properties of Triangles

In a $\triangle A B C,(a-b)^2 \cos ^2 \frac{C}{2}+(a+b)^2 \sin ^2 \frac{C}{2}$ is equal to

A $a^2$
B $c^2$
C $b^2$
D $a^2+b^2$

Verified Solution

Answer & Solution

Correct Answer

(B) $c^2$

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

If $A, B, C$ are three events of a sample space such that $P(B)=\frac{3}{2} P(A)$ and $P(C)=\frac{1}{2} P(B)$ then which of the following is correct?

TS EAMCET 2020 Medium
The coordinates of a point on the curve $x=a(\theta+\sin \theta), y=a(1-\cos \theta)$ where the tangent is inclined at an angle $\frac{\pi}{4}$ to the positive $X$-axis, are

TS EAMCET 2019 Medium
Suppose the axes $X$ and $Y$ are obtained by rotating the axes $x$ and $y$ an angle $\theta$. If the equation $x^2+2 \sqrt{3} x y-y^2=4 a^2$ is transformed to $X^2-Y^2=2 a^2$ with respect to the $X Y$-axes, then $\theta$ is equal to

TS EAMCET 2020 Hard
If the coefficients $a$ and $b$ of $a$ quadratic expression $x^2+a x+b$ are choosen from the sets $A=\{3,4,5\}$ and $\mathrm{B}=\{1,2,3,4\}$ respectively, then the probability that the equation $x^2+a x+b=0$ has real roots is

TS EAMCET 2023 Easy
If $F_1$ and $F_2$ are irreducible factors of $x^4+x^2+1$ with real coefficients and $\frac{x^3-2 x^2+3 x-4}{x^4+x^2+1}=\frac{A x+B}{F_1}+\frac{C x+D}{F_2}$, then $A+B+C+D=$

TS EAMCET 2018 Medium
$\mathbf{a}=\mathbf{i}+\mathbf{j}-2 \mathbf{k} \Rightarrow \sum\{(\mathbf{a} \times \mathbf{i}) \times \mathbf{j}\}^2$ is equal to

TS EAMCET 2012 Easy

Explore more questions on app

From TS EAMCET

Which of the following is a zero order reaction?

TS EAMCET 2022 Easy
$2.0 \mathrm{~g}$ of a non-electrolyte dissolved in $100 \mathrm{~g}$ of benzene lowers the freezing point of benzene by $1.2 \mathrm{~K}$. The freezing point depression constant of benzene is $5.12 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$. The molar mass of the solute is

TS EAMCET 2018 Easy
A unit vector coplanar with $\mathbf{i}+\mathbf{j}+3 \mathbf{k}$ and $\mathbf{i}+3 \mathbf{j}+\mathbf{k}$ and perpendicular to $\mathbf{i}+\mathbf{j}+\mathbf{k}$ is

TS EAMCET 2013 Medium
For $\ell \in \mathbb{R}$, the equation $(2 \ell-3) \mathrm{x}^2+2 \ell \mathrm{xy}-\mathrm{y}^2=0$ represents a pair of distinct lines

TS EAMCET 2023 Easy
If the mean and variance of a binomial distribution are $4$ and $\frac{4}{3}$ respectively, then $P (X = 2) =$

TS EAMCET 2022 Medium
A triangle is formed by $Y$-axis, the straight line $L$ passing through the points $(3,0),\left(1, \frac{4}{3}\right)$ and the straight line perpendicular to the line $L$ and passing through the point $(8,1)$. Then, the area of the triangle (in sq units) is

TS EAMCET 2018 Easy

Explore more questions on app

In a \(\triangle A B C,(a-b)^2 \cos ^2 \frac{C}{2}+(a+b)^2 \sin ^2 \frac{C}{2}\) is equal to

Answer & Solution

Step-by-step Solution

See the Complete Solution