If f (θ) = tan θ and f (a) = 2, find the exact value of:

Question

Use the periodic and even–odd properties.

If f (θ) = tan θ and f (a) = 2,  find the exact value of:

(a) f (- a)               (b) f (a) + f (a + π) + f (a + 2π)

Answer 1

Step 1:

The functions are and .

If then

(a)

Find .

Substitute in .

Use even-odd properties :.

.

Step 2:

(b)

Find .

        ( Since )

Use periodic properties : .

                            ( Since )

                                             

.

Solution :

(a) .

(b) .