**Problem : **
Solve the following equation: sin(*x*)tan(*x*) = 0.

Solving

sin(*x*) = 0,

*x* = 0, *Π*. Solving

tan(*x*) = 0, the same solutions
are reached.

*x* = 0, *Π*.

**Problem : **
Solve the following equation: cos(*x*) - tan^{2}(*x*) = 1.

Using the identity

1 + tan^{2}(*x*) = sec^{2}(*x*), the equation

cos^{3}(*x*) = 1
results. Therefore

cos(*x*) = 1, and

*x* = 0.

**Problem : **
Solve the following equation: sin^{2}(*x*) - 1 = cos^{2}(*x*) + 2.

Using the identity

sin^{2}(*x*) + cos^{2}(*x*) = 1, the equation

sin^{2}(*x*) = 2
results. This equation has no solution.

**Problem : **
Solve the following equation: 2 sec(*x*)sin^{3}(*x*) = cos(*x*)tan^{2}(*x*).

Resolving everything into sines and cosines and then cancelling, we have

sin(*x*) = .

*x* = ,.

**Problem : **
Solve the following equation: sin(*x*) + sin(*x*)cot^{2}(*x*) = sec^{2}(*x*) - tan^{2}(*x*).

Factoring on the right side and the use of identities leads to the equations

sin(*x*) = 1. Therefore,

*x* = .