Question

Cos 75гр * cos 105гр=?

Answer 1

COS75*COS105=C0S(90-15)*COS(90+15)=(COS90*COS15+SIN90*SIN15)(C0S90COS15-SIN90SIN15)=(SIN15)(-SIN15)=-SIN²15=(COS30-1)/2=0,5√3-0,5







C0S15
=

Answer 2

We can use the identity cos(A)*cos(B) = (1/2)[cos(A-B)+cos(A+B)] to solve this problem.

Let A = 75 degrees and B = 105 degrees. Then:

cos(A-B) = cos(75-105) = cos(-30) = cos(30) = √3/2 cos(A+B) = cos(75+105) = cos(180) = -1

Therefore, cos(A)*cos(B) = (1/2)[cos(A-B)+cos(A+B)] = (1/2)[√3/2 - 1] ≈ -0.306.

Hence, cos 75гр * cos 105гр ≈ -0.306.