Show that `cos 2A=cos^(2)A-sin^(2)A`

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

cos (A+B).cos(A-B)=cos^(2)A-sin^(2)B

cos (A+B).cos(A-B)=cos^(2)A-sin^(2)B

Show that cos 36^(@) cos 54 ^(@) -sin 36^(@) sin 54^(@) =0

Prove that: (sin A + cos A)/(sin A - cos A) + (sin A - cos A)/(sin A + cos A) = (2)/(sin^(2)A-cos^(2)A)=(2)/(2sin^(2)A-1)=(2)/(1-2 cos^(2)A) .

Prove that (cos x +cos y)^(2)+(sin x-sin y)^(2)=4 cos^(2) ((x+y)/(2))

If y=x+tan x , show that cos^(2) x. (dy)/(dx)=2-sin^(2)x .