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 = .