Prove that: `cos(45^(@)+A) cos(45^(2)-A)=1/2 cos2A`

Prove that: cos(45^(@)+A) cos(45^(@)-A)=1/2 cos2A

Prove that: sin(45^(@)-A)=1/2cos2A

Prove that: cos(45^(@)-A)cos(45^(@)-B)-sin(45^(@)-A)sin(45^(@)-B)=sin(A+B)

Prove that: sin(45^(@)-A)sin(45+A)=1/2cos2A

Prove that cos (30^(@) -A ) cos (30^(@) + A ) + cos (45^(@) - A) cos (45^(@) + A) = cos 2A + (1)/(4) .

Prove that sin(45^@+A)sin(45^@-A)=1/2cos2A.

Prove that (cos45^@ + isin45^@)^2 = i

2sin45^(@)cos45^(@)

Prove that: (i) cos^(2)30^(@),cos^(2)45^(@),cos^(2)60^(@) are in A.P. (ii) cot^(2)30^(@),cot^(2)45^(@),cot^(2)60^(@) are in G.P.

Value of cos(45^@ +x) + cos(45^@-x) =