Let A,B,C,D be positive angles such that `A+B+C+D =180^@` show that `sinAsinB+sinC*sinD=sin(B+C)*sin(B+D)`

If A+B+C=180^(@), show that sin2A-sin2B-sin2C=-4sin A cos B cos C

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

If A + B + C =180^@ , prove that : sin^2 A- sin^2 B+ sin^2 C=2 sin A cos B sinC .

If A,B,C be the angles ofa triangle then prove that (sin A + sin B)(sin B + sin C)(sinC + sinA) gt sin A sin B sinC .

If A,B,C are the angle of a triangle then the value of determinant |(sin2A,sinC,sinB),(sinC,sin2B,sinA),(sinB,sinA,sin2C)| is a) pi b) 2lambda c)0 d)None of these

In a scalene triangle A B C ,D is a point on the side A B such that C D^2=A D * D B , sin sin A * Sin B=sin^2C/2 then prove that CD is internal bisector of /_Cdot

In a scalene triangle A B C ,D is a point on the side A B such that C D^2=A D *D B , sin A * sin B=sin^2(C/2) then prove that CD is internal bisector of /_C

If A,B and C are the angle of a triangle show that |{:(sin2A,sinC,sinB),(sinC,sin2B,sinA),(sinB,sinA,sin2C):}|=0.

If A,B and C are the angle of a triangle show that |{:(sin2A,sinC,sinB),(sinC,sin2B,sinA),(sinB,sinA,sin2C):}|=0.

If A + B + C =180^@ , prove that : sin (B+C-A) + sin(C+ A-B)+ sin(A +B-C)=4sin A sinB sinC .