Here's the first one.

When faced with trig problems like these, what you want to do is first see if any trig identities can siplify things a bit. If not, treat each trig function as a variable, and facter as you would normally. for instance, the first one is:

tan^2x - 4tanx = 0

if we thought of tangent as a variable, say y, the problem would become:

y^2 - 4y = 0

that's a regular quadratic equation, you should have no problem with that. that is the basis of how i approached the problem. try the second one and tell me if you get it

EDIT: i see that you changed question 1. anyway, it doesn't matter, the same method is applicable. try them