If `A+B+C=pi/2` show that

If A+B+C = pi show that cos^2 (A/2)-cos^2 (B/2)-cos^2 (C/2)=-2sin(A/2)cos(B/2)cos(C/2)

If A+B+C =pi , show that cot A + cot B+cot C-cosec A *cosec B* cosec C = cot A*cot B*cot C .

If A+B+C = pi , show that |["sin"^(2)A, "sin A cos A", "cos"^(2)A],["sin"^(2) B, "sin B cos B", "cos"^(2)B],["sin"^(2)C, "sin C cos C", "cos"^(2)C]| =-"sin (A-B)"sin"(B-C)"sin"(C-A)"

If A+B+C=pi , show that : 1/2 sum sin^2 A (sin 2B+sin 2C) = 3 sin A sin B sin C .

If A+B+C=pi , show that : 1/2 sum sin^2 A (sin 2B+sin 2C) = 3 sin A sin B sin C .

If A + B= pi/4 , show that (cot A-1) (cot B-1) =2

If A+B+C=pi, show that : tan.(A)/(2)tan.(B)/(2)+tan.(B)/(2)tan.(C)/(2)+tan.(C)/(2)tan.(A)/(2)=1 Hence deduce that : cot.(A)/(2)+cot.(B)/(2)+.cot.(C)/(2)=cot.(A)/(2).cot.(B)/(2)tan.(C)/(2) .

If A+B+C+D=2pi , show that : cosA-cosB+cosC-cosD=4sin( (A+B)/(2)) sin( (A+D)/(2)) cos( (A+C)/(2)) .

If A+B+C+D=2pi , show that : cosA-cosB+cosC-cosD=4sin( (A+B)/(2)) sin( (A+D)/(2)) cos( (A+C)/(2)) .

If A+B+C = 2pi , show that sin^(3)A+sin^(3)B + sin^(3)C = 3sin A/2* sin B/2* sin C/2 - sin3A/2*sin 3B/2 * sin3C/2