Question:
In any $\Delta ABC$, $a(b \cos C-c \cos B)$ equals
In any $\Delta ABC$, $a(b \cos C-c \cos B)$ equals
Show Hint
Standard cosine rule: $\cos C = \frac{a^2+b^2-c^2}{2ab}$.
Updated On: Apr 10, 2026
- $b^{2}+c^{2}$
- $b^{2}-c^{2}$
- $\frac{1}{b}+\frac{1}{c}$
- $\frac{1}{b^{2}}-\frac{1}{c^{2}}$
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Expand
$ab \cos C - ac \cos B$.
Step 2: Cosine Rule
$ab(\frac{a^2+b^2-c^2}{2ab}) - ac(\frac{a^2+c^2-b^2}{2ac})$.
Step 3: Simplify
$\frac{a^2+b^2-c^2}{2} - \frac{a^2+c^2-b^2}{2} = \frac{2b^2 - 2c^2}{2} = b^2 - c^2$.
Final Answer: (B)
$ab \cos C - ac \cos B$.
Step 2: Cosine Rule
$ab(\frac{a^2+b^2-c^2}{2ab}) - ac(\frac{a^2+c^2-b^2}{2ac})$.
Step 3: Simplify
$\frac{a^2+b^2-c^2}{2} - \frac{a^2+c^2-b^2}{2} = \frac{2b^2 - 2c^2}{2} = b^2 - c^2$.
Final Answer: (B)
Was this answer helpful?
0
0
Top MET Mathematics Questions
- $\int\limits_{0}^{8}| x -5| d x$ is equal to
- The equation $3^{3x + 4} = 9^{2x - 2},\ x>0$ has the solution
- A parallelogram is constructed on the vectors $\mathbf{a} = 3\alpha - \beta$, $\mathbf{b} = \alpha + 3\beta$. If $|\alpha| = |\beta| = 2$ and the angle between $\alpha$ and $\beta$ is $\dfrac{\pi}{3}$, then the length of a diagonal of the parallelogram is
- Every group of order 7 is
- Let $U_{n} = 2 + 2^{3} + 2^{5} + \cdots + 2^{2n+1}$ and $V_{n} = 1 + 4 + 4^{2} + \cdots + 4^{n-1}$. Then $\displaystyle\lim_{n \to \infty} \dfrac{U_n}{V_n}$ is equal to
View More Questions
Top MET Trigonometry Questions
- If $\tan^{-1}x + \tan^{-1}y + \tan^{-1}z = \pi$, then $x + y + z$ is
- If $3\sin^{-1}\!\left(\dfrac{2x}{1+x^{2}}\right) - 4\cos^{-1}\!\left(\dfrac{1-x^{2}}{1+x^{2}}\right) + 2\tan^{-1}\!\left(\dfrac{2x}{1-x^{2}}\right) = \dfrac{\pi}{3}$, then $x$ equals
- If $\sin(\pi \cos \theta) = \cos(\pi \sin \theta)$, then which of the following is correct?
- $\sin^{-1}\dfrac{1}{\sqrt{5}} + \cos^{-1}\dfrac{3}{\sqrt{10}}$ is equal to
- If $4\sin^{-1}x + \cos^{-1}x = \pi$, then $x$ is equal to
View More Questions
Top MET Questions
- A coil of 100 turns and area $2 \times 10^{-2}m^2 $ is pivoted about a vertical diameter in a uniform magnetic field and carries a current of 5A. When the coil is held with its plane in north-south direction, it experiences a couple of 0.33 Nm. When the plane is east-west, the corresponding couple is 0.4 Nm, the value of magnetic induction is [Neglect earth's magnetic field]
- $\int\limits_{0}^{8}| x -5| d x$ is equal to
- Radiation, with wavelength 6561 $?$ falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of $3 \times 10^{-4} T$. If the radius of the largest circular path followed by the electrons is 10 mm, the work function of the metal is close to :
- In intrinsic semiconductor at room temperature number of electrons and holes are
- Which of the following product is formed in the reaction $ CH_3MgBr {->[(i)CO_2][(ii)H_2O]} ? $
View More Questions