Home
Class 11
MATHS
If A+B+C =pi , prove that sin 2A+sin...

If `A+B+C =pi ,` prove that
`sin 2A+sin 2B+sin 2C=4 sin Asin B sin C.`

Text Solution

AI Generated Solution

To prove that \( \sin 2A + \sin 2B + \sin 2C = 4 \sin A \sin B \sin C \) given that \( A + B + C = \pi \), we can follow these steps: ### Step 1: Use the identity for sine of a sum We know that: \[ \sin 2A = 2 \sin A \cos A \] \[ ...
Promotional Banner

Topper's Solved these Questions

  • CONDITIONAL IDENTITIES INVOLVING THE ANGLES OF A TRIANGLE

    RS AGGARWAL|Exercise EXERCISE 16|12 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    RS AGGARWAL|Exercise EXERCISE 5 G|28 Videos

  • DIFFERENTIATION

    RS AGGARWAL|Exercise Exercise 28E|44 Videos

Similar Questions

Explore conceptually related problems

If A+B+C=pi , prove that sin 2A-sin 2B+sin 2C=4cos Asin B cos C.

If A+B+C=pi , prove that sin 2A+sin 2B-sin 2C=4 cos A cos B sin C

If A+B+C=pi , prove that : sin2A+sin2B+sin2C=4sinA sinB sinC

If A+B+C =180^(@) then prove that sin 2A + sin 2B+ sin 2C = 4 sin A sin B sin C

Theorem 1:sin2A+sin2B+sin2C=4sin A sin B sin C

If A+B+C=pi , prove that : (sin 2A+sin 2B + sin 2C)/(sinA+sinB+sinC) = 8 sin(A/2) sin(B/2) sin(C/2)

If A+B+C=180^(@), then prove that sin2A+sin2B+sin2C=4sin A sin B sin C

If A+B+C=0^(@) then prove that sin2A+sin2B+sin2C=-4sin A sin B sin C

If A+B+C=pi then prove that sin2A-sin2B+sin2C=4cos A sin B cos C

If A+B+C= pi/2 ,prove that: sin2A-sin2B+sin2C=4sinAcosBsinC