Trigonometric Sum and Difference Example Post

1). Find sin (60º-45º)

Employing sin(a-b) = sin(a)cos(b) - sin(b)cos(a)

sin(60º-45º) = sin(60º)cos(45º) - sin(45º)cos(60º)

=(√(3)/2)(√(2)/2) - (√(2)/2)(1/2)

=(√6 - √2)/4

2). Find cos(-x)

Employing cos(2π-x) = cos(-x) and cos(a-b) = cos(a)cos(b) - sin(a)sin(b) we have:

cos(-x) = cos(2π-x)

= cos(2π)cos(x) - sin(2π)sin(x)

= (1)cos(x) - (0)sin(x)

= cos(x)

Voilà!