JEE MATHEMATICS MCQ: PROPERTIES OF TRIANGLES

1 Easy

1 of 1

Application +4 | -1

In a

\Delta \,ABC,\,\,{\cos ^2}\,\,\frac{A}{2}\,\, + \,\,{\cos ^2}\,\,\frac{B}{2}\, + \,{\cos ^2}\,\,\frac{C}{2} =

View answer and explanation

Correct option: C

2 + \frac{r}{{2R}}

Option C (

2 + \frac{r}{{2R}}

) is correct because the expression

{\cos ^2}\,\frac{A}{2}\, + \,{\cos ^2}\,\frac{B}{2}\, + \,{\cos ^2}\,\frac{C}{2}

simplifies to

2 + \frac{r}{{2R}}

using trigonometric identities and the relationship between inradius and circumradius.

More Questions from PROPERTIES OF TRIANGLES

Practice All Chapter MCQs →

{p_1},{p_2},{p_3}

\Delta \;ABC

A,B,C

\Delta

p_1^{ - 2} + p_2^{ - 2} + p_3^{ - 2}

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