In A B C, with usual notations, 2 a c (1 2 (A-B+C) ) is equal to - Vidyadip

MCQ

In $\triangle A B C$, with usual notations, $2 a c \sin \left(\frac{1}{2}(A-B+C)\right)$ is equal to

A
$a^2+b^2-c^2$
✓
$c^2+a^2-b^2$
C
$b^2-c^2-a^2$
D
$c^2-a^2-b^2$

✓

Answer

Correct option: B.

$c^2+a^2-b^2$

(b) : In $\triangle A B C$, we have $A+B+C=180^{\circ}$ ...(i)
Now, $2 a c \sin \left(\frac{A-B+C}{2}\right)$
$
\begin{aligned}
& =2 a c \sin \left(\frac{180^{\circ}-2 B}{2}\right) \quad \text { [Using (i)] } \\
& =2 a c \sin \left(90^{\circ}-B\right)=2 a c \cos B \\
& =2 a c\left(\frac{c^2+a^2-b^2}{2 a c}\right)=c^2+a^2-b^2
\end{aligned}
$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from Trigonometric Functions→Trigonometric Functions — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

The order of the differential whose general solution is given by ${\text{y}}=\text{C}_1\cos(2\text{x}+\text{C}_{2})+(\text{C}_{3}+\text{C}_{4})\text{a}^{\text{x}+\text{C}_{5}}+\text{C}_{6}\sin(\text{x}-\text{C}_{7}).$

The value of $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{\sin ^2 x}{1+2^x} d x$ is

Let $\theta$ be the angle between the lines AB and AC , where $A , B$ and C are the three points with co-ordinates $(1,2,-1),(2,0,3),(3,-1,2)$ respectively, then $\sqrt{462} \cos \theta$ is equal to

If $X \sim B(4, p)$ and $P(X=0)=\frac{16}{81}$, then $P(X=4)=$

The equation of the plane through $(-1,1,2)$, whose normal makes equal acute angles with co-ordinate axes is

If $P$ and $q$ are the order and degree of the differention $\text{y}\frac{\text{dy}}{\text{dx}}+\text{x}^{3}\frac{\text{d}^{2}\text{y}}{\text{dx}^{3}}+\text{xy}=\cos\text{x}$ then:

The principal value branch of $\sec ^{-1} x$ is

If the points $P (\overline{ a }+2 \overline{b}+\overline{ c }), Q (2 \overline{ a }+3 \overline{b})$ and $R (\overline{ b }+ t \overline{ c })$ are collinear, where $\overline{ a }, \overline{ b }, \overline{ c }$ are three non-coplanar vectors, then the value of $t$ is

If sum of all the solutions of the equation $8 \cos x \cdot\left[\cos \left(\frac{\pi}{6}+x\right) \cdot \cos \left(\frac{\pi}{6}-x\right)-\frac{1}{2}\right]=1 \ in$ $[0, \pi]$ is $k \pi$, then k is equal to

If the acute angle between the lines $x^2-4 h x y+3 y^2=0$ is $60^{\circ}$ then $h =$