Question

Verify that cos (270° - q) = -sin q is an identity.

Answer 1

In order to verify this identity we can expand and simplify the left hand side of the equation. If it becomes equal to the right hand side, this will prove theat the given equation is an identity.

Left hand side = cos (270 - q)
= cos(270)sin(q) + sin(270)cos(q)

cos(270) = -1
sin(270) = 0

So the left hand side becomes
= -1*sin(q) + 0*cos(q)
= - sin(q)
= Right Hand side

This proves the left hand side is equal to the right hand side and so given equation is an identity which means it is true for all values of q.