In a triangle ABC,if a cos^2 frac{C}{2} + c c | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given: $a \cos^2 \frac{C}{2} + c \cos^2 \frac{A}{2} = \frac{3b}{2}$ Using the half-angle formulas $\cos^2 \frac{C}{2} = \frac{s(s-c)}{ab}$ and $\c

Vedclass · Accepted Answer

an arithmetic progression

Vedclass · Answer

(A) Given: $a \cos^2 \frac{C}{2} + c \cos^2 \frac{A}{2} = \frac{3b}{2}$ Using the half-angle formulas $\cos^2 \frac{C}{2} = \frac{s(s-c)}{ab}$ and $\cos^2 \frac{A}{2} = \frac{s(s-a)}{bc}$: $a \cdot \frac{s(s-c)}{ab} + c \cdot \frac{s(s-a)}{bc} = \frac{3b}{2}$ $\frac{s(s-c)}{b} + \frac{s(s-a)}{b} = \frac{3b}{2}$ $\frac{s}{b} (s - c + s - a) = \frac{3b}{2}$ Since $2s = a + b + c$,we have $2s - a - c = b$: $\frac{s}{b} (b) = \frac{3b}{2}$ $s = \frac{3b}{2} \Rightarrow 2s = 3b$ Substituting $2s = a + b + c$: $a + b + c = 3b$ $a + c = 2b$ Thus,$a, b, c$ are in arithmetic progression.

In a $\triangle ABC$,if $a \cos^2 \frac{C}{2} + c \cos^2 \frac{A}{2} = \frac{3b}{2}$,then the sides of the triangle are in

Similar Questions

Manganese inhibits calcium translocation in........

Which of the following salts gives a white precipitate with $AgNO_3$ solution and dilute $H_2SO_4$ solution,and also gives a green flame test?

In the circuit shown,the current in the $1\,\Omega$ resistor is

Which bacteria can survive in water at temperatures exceeding $100 \, ^\circ C$?

When a non-volatile solute is added to a solvent,the vapor pressure decreases by $10 \ mm$. The mole fraction of the solute is $0.2$. If the vapor pressure decreases by $20 \ mm$,what will be the mole fraction of the solvent?

Vedclass Test Series

Exam Paper Generator

Online Exam Module