Well, [tex]\theta= tan^{-1} \frac{b}{x}[\math] if and only if is an angle in a right triangle with "opposite side" of length a and "near side" of length x. Similarly, if if and only if [itex]\phi[/itex] is an angle in a right triangle with "opposite side" b and "near side" x. Now, imagine those two triangles sharing the side of length x. You have a triangle with angle , base of lenght a+b and altitude of length x. Unfortunately, I don't really see where to go from there.

Find the value of x.

This doesn't seem to be striking me at all. I used the trigonometry identity of tan inverse A + tan inverse B, but the answer doesn't really spring from that..

Any help will be appreciated.

Also,

Find the value of the expression here. I tried substituting and converting cos inverse to sin inverse but the identity is becoming too long and the answer ambiguous.[/QUOTE]