Prove the following:If`tanA=1/2,tanB=1/3` ,prove that `cos2A=sin2B`

If tanA=1/2 , tanB=1/3 , then cos2A=

If tanA=5/6,tanB=1/11 prove that A+B=pi/4

Prove the following:If tanA=2tanB+cotB ,then 2tan(A-B)=cotB

Prove the following: if A+B=225^@ ,then prove that (frac(cotA)(1+cotA)).(frac(cotB)(1+cotB))=1/2

Solve the following: If A+B+C=pi ,prove that sin(B+2C)+sin(C+2A)+sin(A+2B)= 4sin((B-C)/2)sin((C-A)/2)sin((A-B)/2)

Solve the following: With usual notations prove that frac{sin(A-B)}{sin(A+B)} = frac{a^2-b^2}{c^2}

Prove the following: cottheta(1-cos2theta)=sin2theta

Solve the following: In /_\ABC prove that cos(frac{A-B}{2}) = frac{a+b}{c}sin(frac{C}{2})

Solve the following: In /_\ABC prove that (a-b)^2cos^2(frac{C}{2})+(a+b)^2sin^2(frac{C}{2}) = c^2