Home
Class 11
MATHS
In DeltaABC, prove that: sin2A+sin2B+s...

In `DeltaABC`, prove that:
`sin2A+sin2B+sin2C=4sinAsinBsinC`

Text Solution

AI Generated Solution

To prove that in triangle \( ABC \), the equation \( \sin 2A + \sin 2B + \sin 2C = 4 \sin A \sin B \sin C \) holds true, we can follow these steps: ### Step 1: Use the angle sum property of triangles In triangle \( ABC \), we know that: \[ A + B + C = 180^\circ \quad \text{(or } \pi \text{ radians)} \] From this, we can express \( C \) as: ...
Promotional Banner

Topper's Solved these Questions

  • TRIGNOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise EXERCISES 3A|12 Videos
  • TRIGNOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise EXERCISES 3B|24 Videos
  • STRAIGHT LINES

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise|207 Videos

Similar Questions

Explore conceptually related problems

In DeltaABC ,prove that: sin2A + sin2B-sin2C=4cosA cosB sinC

Prove that sin2A + sin2B + sin2C = 4sinA · sinB · sin C

In DeltaABC ,prove that: a) sin2A + sin2B-sin2C=4cosA cosB sinC

In DeltaABC , prove that: a) (sin2A + sin2B + sin2C)/(sinA+sinB+sinC) = 8sin(A/2) sin(B/2)sin(C/2)

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

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

If DeltaABC , prove that: a) sin^(2)A+sin^(2)B-sin^(2)C=2sinAsinBcosC b) cos^(2)A+cos^(2)B-cos^(2)C=1-2sinAcosBsinC c) cos^(2)A+cos^(2)B+cos^(2)C=1-2cosAcosBcosC

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

In DeltaABC , prove that: sin^(2)A+sin^(2)B+sin^(2)C =2+2cosAcosBcosC.

In a DeltaABC , prove that : sin3A sin(B-C)+sin3B sin(C-A) + sin3C sin (A-B)=0 .