JEE MATHEMATICS MCQ: PROPERTIES OF TRIANGLES

1 Easy

1 of 1

Application +4 | -1

If in a

\triangle A B C, a \cos ^2\left(\frac{C}{2}\right)+c \cos ^2\left(\frac{A}{2}\right)=\frac{3 b}{2}

, then the sides

a, b

and

c

View answer and explanation

Correct option: A

are in AP

Option A (are in AP) is correct because by substituting the half-angle formula into the given equation and simplifying, we can show that

2b = a+c

, which means

a, b, c

are in arithmetic progression.

More Questions from PROPERTIES OF TRIANGLES

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{p_1},{p_2},{p_3}

\Delta \;ABC

A,B,C

\Delta

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5k,\;6k,\;5k

k

\Delta \,ABC

a = \left( {b - c} \right)\sec \theta

\frac{{2\,\sqrt {bc} }}{{b - c}}\,\,\sin \,\,\frac{A}{2} =

\Delta \;ABC,\frac{{b + c}}{a}

\Delta = {a^2} - {\left( {b - c} \right)^2}

\Delta

\Delta \;ABC

\tan A

A

2 s