In △ ABC if cos A + 2 cos B + cos C = 2 , then the value of b 2 s (where ' s ' is the semi peri meter) is

cos A + cos C = 2 ( 1 − cos B ) ⇒ 2 cos 2 A + C cos 2 A − C = 2 × 2 sin 2 2 B ⇒ s i n 2 B c o s ( 2 A − C ) = 2 ⇒ b a + c = 2 ⇒ a + c = 2 b ∴ b 2 S = b 3 b = 3

Start Free Mock LoginAlready registered? Login here

Mathematics - Properties of Triangle Question with Solution | TestHub

MathematicsProperties of TriangleGeneral (basic formula based)Easy2 minQB

MathematicsEasyinteger

In $△ ABC$ if $cos A + 2 cos B + cos C = 2$ , then the value of $\frac{2 s}{b}$ (where ' s ' is the semi peri meter) is

Answer:

Solution:

$cos A + cos C = 2 (1 - cos B)$

$\Rightarrow 2 cos \frac{A + C}{2} cos \frac{A - C}{2} = 2 \times 2 sin^{2} \frac{B}{2}$

$\Rightarrow \frac{c o s ( \frac{A - C}{2} )}{s i n \frac{B}{2}} = 2 \Rightarrow \frac{a + c}{b} = 2 \Rightarrow a + c = 2 b$

$∴ \frac{2 S}{b} = \frac{3 b}{b} = 3$

Stream:JEESubject:MathematicsTopic:Properties of TriangleSubtopic:General (basic formula based)

⏱ 2mℹ️ Source: QB

Doubts & Discussion

Loading discussions...