Problems

In Problems 1-6, derive the given identity using the formula sin² θ + cos² θ = 1 and the addition formulas for sin (θ + φ) and cos (θ + φ).

In Problems 7-10, find all values of θ for which the given equation is true.

11           Find a value of θ where sin 2θ is not equal to 2 sin θ.

Determine whether the limits exist in Problems 12-17.

18            Find all values of θ where tan θ is undefined.

19            Find all values of θ where csc θ is undefined.