Home
Class 12
MATHS
If A+B+C=pi, prove that : sin (B+C-A) + ...

If `A+B+C=pi`, prove that : `sin (B+C-A) + sin (C+A-B) + sin (A+B-C)=4sinA sinB sinC`

Text Solution

AI Generated Solution

Promotional Banner

Similar Questions

Explore conceptually related problems

sin(B+C-A)+sin(C+A-B)+sin(A+B-C)=4sin A sin B sin C

If A + B + C = 180^(@) prove that: (i) "sin" (B+C-A) + "sin"(C+ A-B) + sin (A + B-C) = 4 sin A sin B sin C (ii) cos(- A+B+C) + cos (A - B + C) + cos (A + B - C) = 1 + 4 cos A cos B cos C (iii) "tan" (B+C - A) + tan (C+A-B) + tan (A + B-C) = tan (B+C - A) tan (C+ A - B) tan (A+B-C)

In triangle ABC, prove that sin(B+C-A)+sin(C+A-B)+sin(A+B-C)=4sin A sin B sin C .

If A+B+C=pi , prove that : sinA cosB cosC +sinB cosC cosA + sinC cosA cosB = sinA sinB sinC .

If A+B+C=pi , Prove that : sin( A/2) + sin( B/2) + sin(C/2) =1 + 4 sin( (B+C)/(4)) sin( (C+A)/(4)) sin( (A+B)/(4))

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=pi , prove that : sin ((B+C)/(2)) + sin ((C+A)/(2)) + sin( (A+B)/(2) )= 4cos ((pi-A)/(4)) cos( (pi-B)/(4)) cos((pi-C)/(4)) .

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= pi/2 , show that : sin^2 A + sin^2 B + sin^2 C=1-2 sinA sinB sinC