To find the value of cos^2(150) - sin^2(120), we first need to determine the cosine and sine values of the given angles.
cos(150 degrees) = cos(180 - 30) = -cos(30) = -√3/2sin(120 degrees) = sin(180 - 60) = sin(60) = √3/2
Now, we can calculate the expression:
cos^2(150) - sin^2(120) = (-√3/2)^2 - (√3/2)^2= 3/4 - 3/4= 0
Therefore, cos^2(150) - sin^2(120) = 0.
To find the value of cos^2(150) - sin^2(120), we first need to determine the cosine and sine values of the given angles.
cos(150 degrees) = cos(180 - 30) = -cos(30) = -√3/2
sin(120 degrees) = sin(180 - 60) = sin(60) = √3/2
Now, we can calculate the expression:
cos^2(150) - sin^2(120) = (-√3/2)^2 - (√3/2)^2
= 3/4 - 3/4
= 0
Therefore, cos^2(150) - sin^2(120) = 0.