Question

If cos (A+B) = cosAcos B – sinAsin B , find the value of cos 75

Answer 1

Explanation:

Cos 75 = Cos ( 30 + 45) {Use Cos (A + B) identity}

= Cos 30*cos 45 - Sin 30 Sin 45

`= (√(3))/(2)*(1)/(√(2))-(1)/(2)*(1)/(√(2))\\\\= (√(3))/(2√(2))-(1)/(2√(2))\\\\=(√(3)-1)/(2√(2))\\\\=((√(3)-1)*√(2))/(2√(2)*√(2))\\\\=(√(3)*√(2)-√(2))/(2*2)\\\\=(√(6)-√(2))/(4)`