If $A + B + C = 270 °$ then $\cos 2 A + \cos 2 B + \cos 2 C + 4 \sin A \sin B \sin C =$

see full answer

High-Paying Jobs That Even AI Can’t Replace — Through JEE/NEET

🎯 Hear from the experts why preparing for JEE/NEET today sets you up for future-proof, high-income careers tomorrow.

An Intiative by Sri Chaitanya

answer is B.

(Unlock A.I Detailed Solution for FREE)

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

A + B + C = 270 °

then

\cos 2 A + \cos 2 B + \cos 2 C + 4 \sin A \sin B \sin C

$= 2 \cos (A + B) . \cos (A - B) + 1 - 2 \sin^{2} C + 4 \sin A . \sin B . \sin C$

$= - 2 \sin C . \cos (A - B) - 2 \sin^{2} C + 1 + 4 \sin A . \sin B . \sin C$

$= - 2 \sin C . (\cos (A - B) + \sin C) + 1 + 4 \sin A . \sin B . \sin C$

$= - 2 \sin C . (\cos (A - B) - \cos (A + B)) + 1 + 4 \sin A . \sin B . \sin C$

$= - 2 \sin C (2 \sin A . \sin B) + 1 + 4 \sin A . \sin B . \sin C$

$= - 4 \sin A . \sin B . \sin C + 1 + 4 \sin A . \sin B . \sin C$

$= 1$

Watch 3-min video & get full concept clarity

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test