If A + B + C = 180°, then what is sin 2A – sin 2B – sin 2C equal

1.	If A + B + C = 180°, then what is sin 2A – sin 2B – sin 2C equal to? a. –4 sin A sin B sin C b. –4 cos A sin B cos C c. –4 cos A cos B sin C d. –4 sin A cos B cos C
Answer» Correct option d. –4 sin A cos B cos C Explanation: sin 2A - sin 2B - sin 2C = 2cos (A + B) sin (A - B) sin( 2A + 2B) = 2cos(A + B) sin(A - B) + 2sin (A + B) cos(A + B) = 2cos(A + B ) [sin(A - B) sin (A + B)] = - 2cosC[ 2sin A cosB] = - 4 sin A cosBcosC

If A + B + C = 180°, then what is sin 2A – sin 2B – sin 2C equal to? a. –4 sin A sin B sin C b. –4 cos A sin B cos C c. –4 cos A cos B sin C d. –4 sin A cos B cos C

Answer»

Correct option d. –4 sin A cos B cos C

Explanation:

sin 2A - sin 2B - sin 2C

= 2cos (A + B) sin (A - B) sin( 2A + 2B)

= 2cos(A + B) sin(A - B) + 2sin (A + B) cos(A + B)

= 2cos(A + B ) [sin(A - B) sin (A + B)]

= - 2cosC[ 2sin A cosB]

= - 4 sin A cosBcosC

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