If tan A ,tan B are the roots of `x^2-bx+c=0`,show that `sin^2(A+B)=b^2/(b^2+(1-c)^2)`

If p be the ratio of roots of the equation ax^2 + bx + c = 0 , show that (p + 1)^2/p=b^2/(ac) .

If alpha and beta are the solution of the equation a tan theta +b sec theta=c ,then show that tan(alpha+beta)=2ac/(a^2-c^2)

If A,B,C are the three angles of a triangle,show that:(iii) sin((B+C)/2)=cos(A/2)

If A,B and C are interior angle of a triangle ABC,then show that sin(B+C)/2=cos(A/2)

If A,B,C are the three angles of a triangle,show that:(iv) tan((B+C)/2)=cot(A/2)

If one root of the equation ax^2+ bx+ c=0 be n times the other,show that (n+1)^2/n=b^2/(ac)

If 2 tan A = 3 tan B.show that tan (A - B)= (sin2B)/(5-cos2B)

If a^2sec^2x-b^2tan^2x=c^2 ,show that cosecx=+-sqrt((b^2-c^2)/(a^2-c^2))

If a,b,c,d are in G.P then show that (b-c)^2+(c-a)^2+(d-b)^2=(a-d)^2 .

If a, b, c are in A.P. then show that the terms given below are also in A.P. (b+c)^2-a^2,(c+a)^2-b^2,(a+b)^2-c^2 .