If in a triangle ABC- a cos2 C2 - c cos2 A2 - 3b2- then the sides of the triangle are in

The correct option is A are in A.P a(1 + cos nbsp;C) + c (1 + cos nbsp;A) = 3b ⇒ a + c + c nbsp;cos nbsp;C + c nbsp;cos nbsp;A = 3b ...

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Standard XII

Mathematics

Conditional Identities

If in a trian...

Question

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

are in A.P

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are in G.P.

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are in H.P.

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Satisfy

a + b = c

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Solution

The correct option is A are in A.P
$a (1 + cos C) + c (1 + cos A) = 3 b$
$\Rightarrow a + c + c cos C + c cos A = 3 b$
$\Rightarrow a + c + b = 3 b \Rightarrow a + c = 2 b$
$\Rightarrow a, b, c$ are in A.P.

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If in a triangle ABC, acos2(C2)+ccos2(A2)=3b2, then the sides of the triangle are in

The correct option is A are in A.Pa(1+cosC)+c(1+cosA)=3b⇒a+c+ccosC+ccosA=3b⇒a+c+b=3b⇒a+c=2b⇒a,b,c are in A.P.

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

The correct option is A are in A.P
$a (1 + cos C) + c (1 + cos A) = 3 b$
$\Rightarrow a + c + c cos C + c cos A = 3 b$
$\Rightarrow a + c + b = 3 b \Rightarrow a + c = 2 b$
$\Rightarrow a, b, c$ are in A.P.