If `A=75^@,B=45^@,` then prove that `b+csqrt(2)=2a`

If tan A=1//2, tan B=1//3 , then prove that cos 2A=sin2B .

If tan(A+B)=3 tan A , prove that (a) sin(2A+B)=2sin B

Prove that 2/(b+c)+2/(c+a)+2/(a+b) 0.

If s intheta,costheta be the roots of a x^2+b x+c=0 , then prove that b^2=a^2+2ac.

If c^(2) = a^(2) + b^(2) , then prove that 4s (s - a) (s - b) (s - c) = a^(2) b^(2)

If a,b,c,d are in geometric sequence then prove that (b-c)^(2) +(c-a)^(2) -(d-b)^(2)=(a-d)^2

If A+B=45^(@)," show that "(1+tan A) (1+tan B)=2 and hence deduce the value of tan"" 22""1^(@)/2 .

If (a ,b) is the midpoint of a chord passing through the vertex of the parabola y^2=4x, then prove that 2a=b^2

If A + B + C = 180^(@) , prove that sin^(2)A + sin^(2)B + sin^(2) C = 2 + 2 cos A cos B cos C