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, prove that sin""(A)/(2)sin""(B)/(2)sin""(C)/(2)le(1)/(8) and hence, prove that co sec ""(A)/(2)+co sec""(B)/(2)+co sec""(C)/(2)ge6 .

In a triangleABC," prove that sin" ((B-C)/(2))=(b-c)/(a) cos""A/2 .

In A B C , prove that (a-b^2cos^2C/2+(a+b)^2sin^2C/2=c^2dot

In a triangleABC, prove that a cos A+b cos B+c cos C=2a sin B sin C

Prove that 4cos(2pi)/7dotcospi/7-1=2cos(2pi)/7dot

In any triangle prove that a^2 =(b+c)^2 sin^2 (A/2) +(b-c)^2 cos^2 (A/2)

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 "=pi

Prove that cos ((3pi)/(4)+x)-cos ((3pi)/(4)-x)=-sqrt2 sin x