State whether the statement is right
A, B, and C are the interior angle of a triangle ABC, then $sin (\frac{B + C}{2}) = cos \frac{A}{2}$

True

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

False

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A True
$A, B, C$ are interior angle of $△ A B C$ then
$A + B + C = π \Rightarrow B + C = π - A \Rightarrow \frac{B + C}{2} = \frac{π - A}{2} \Rightarrow sin (\frac{B + C}{2}) = sin (\frac{π - A}{2}) = sin (\frac{π}{2} - \frac{A}{2}) = cos \frac{A}{2}$

Suggest Corrections

Similar questions

A, B

C

A B C

sin (\frac{B + C}{2}) = cos \frac{A}{2}

s i n (\frac{B + C}{2}) = c o s \frac{A}{2}

A, B

C

A B C

sin (\frac{B + C}{2}) = cos \frac{A}{2} .

sin (\frac{B + C}{2}) =

For a triangle ABC, show that sin $(\frac{B + C}{2})$ = cos $(\frac{A}{2})$ , where A, B and C are interior angles of $△$ ABC.

Join BYJU'S Learning Program