The trigonometric equation is 2 cos x + tan x = sec x.

                                   ()

         (Multiply each side by cos x)

                                              (Simplify)

                    (Apply pythagorean identity: )

                                         (Apply distributive property)

                              (Subtract 1 from each side)

                                      (Simplify)

                              (Take out common factor)

                          (Apply zero product property)

The solutions are .

The trigonometric equation is and the interval is . \ \

Consider .

Apply double angle identity : .

\ \

\ \

\ \

and

and  .

Consider .

The general solution of is , where is an integer. \ \

The general solution is .

If , .

If , .

If , .

If , .

Thus, the solutions are and in the interval .

Consider .

The general solution of is , where is an integer. \ \

The general solution is .

If , .

If , .

If , .

Thus, the solutions of are , , and in the interval .

The solutions of are , , and in the interval .