Question

Find an exact value.

cos 75Á

Answer 1

Use formula
cos(A + B) = cos A cos B − sin A sin B


`cos(75^o) \\ cos((45^o+30^o)) \\ cos(45^o)cos(30^o)-sin(45^o)sin(30^o) \\ ( √(2) )/(2) * ( √(3) )/(2)-( √(2) )/(2) * (1)/(2) \\ ( √(6) )/(4) -( √(2) )/(4) \\ ( √(6)- √(2) )/(4) \\ ( √(2)√(3)- √(2) )/(4) \\ ( √(2)(√(3)- 1 ))/(4)`