`A+ B = C and tan A = k tan B`, then prove that `sin (A-B) = (k-1)/(k+1) sin C`

If tan A= xtanB then prove that sin(A-B)/sin(A+B)=(x-1)/(x+1)

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

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

If tan A = n tan B and sin A = m sin B, prove that : cos^(2) A = (m^(2) - 1)/(n^(2) - 1)

i) If tan (A+B) = n tan (A-B), prove that: (n+1)/(n-1) = (sin2A)/(sin2B)

If cos^2 A - sin^2 A = tan^2 B then prove that 2 cos^2 B -1 = tan^2 A

If cos^2 A - sin^2 A = tan^2 B then prove that 2 cos^2 B -1 = tan^2 A

If cosA=kcos(A-2B) , prove that: tan(A-B)tanB= (1-k)/(1+k)

If cos A + cos B = (1)/(3) and sin A + sin B = 1/4 prove that tan "" (1)/(2) (A+B) = 3/4.

If (tan 3A)/(tan A)=k , show that ( sin 3A)/(sin A)= (2k)/(k-1) and hence or otherwise prove that either k gt 3 or k lt 1/3 .