Prove that `sin^2(A/2)+sin^2(B/2)-sin^2(C/2)=1-2cos(A/2)cos(B/2)sin(C/2)`

A+B+C=pi ,prove that sin^2(A/2)+sin^2(B/2)+sin^2(C/2)=1-2sin(A/2)sin(B/2)sin(C/2)

Prove that sin^2B=sin^2A+sin^2(A-B)-2sinAcosBsin(A-B)

If A+B+C=180^@ then prove that sin( A/2)+sin( B/2)+sin( C/2) = 1+4 sin( (pi-A)/4)sin((pi-B)/4)sin ((pi-C)/4)

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

Prove that in a A B C ,sin^2A+sin^2B+sin^2C<=9/4dot

In triangle A B C , prove that sin(A/2)+sin(B/2)+sin(C/2)lt=3/2dot Hence, deduce that cos((pi+A)/4)cos((pi+B)/4)cos((pi+C)/4)lt=1/8

In triangle ABC , if C is a right prove that (sin^(2)A)/(sin^(2)B)-(cos^(2)A)/(cos^(2)B)=(a^(4)-b^(4))/(a^(2)b^(2))

Prove that (cosA-cosB)^2+(sin A-sin B)^2=4sin^2((A-B)/2)

Compute the following: [(a,b),(-b,a)]+[(a,b),(b,a)] (ii) [(a^(2)+b^(2),b^(2)+c^(2)),(a^(2)+c^(2),a^(2)+b^(2))]+[(2ab,2bc),(-2ac,-2ab)] (iii) [(-1,4,-6),(8,5,16),(2,8,5)]+[(12,7,6),(8,0,5),(3,2,4)] (iv) [(cos^(2)x, sin^(2)x),(sin^(2)x, cos^(2)x)]+[(sin^(2)x, cos^(2)x),(cos^(2)x, sin^(2)x)]

int (sin 2x dx)/(a^(2) sin^(2)x+b^(2) cos^(2)x)