solve tan(2x) = 8 cos^2(x) - cos(x) on [0, pi/2], etc

[Uncle6]

I can't solve this questions nor can my teacher. We are just starting trig equations, so I'm quite new to this as well. Help to the starting steps to solve these would be greatly appreciated.

EDIT OCT11: I got em all, but I'd just like to see other ways of solving that don't involve dividing.

4. Solve for x in the given interval
(d)

tan (2x) = 8cos^2(x) - cot (x) , [0,pi/2]

(e)

tan(x) + sec (2x) = 1 , [-pi/2, pi/2]

6. If tan(2x) = -24/7 , find the values of sin x and cos x

 

[stapel]

Re: Pre-Calc Trig equation

tan (2x) = 8cos^2(x) - cot (x) , [0,pi/2]

I got this now, but i'd like to see any other solutions. My way involves dividing by cosx which I assume is not zero.

It will be difficult to find "other solutions", when we have little idea what your solution was. Sorry!

tan(x) + sec (2x) = 1 , [-pi/2, pi/2]

The secant is the reciprocal of the cosine, so convert to sines and cosines, and apply the double-angle formula to convert the argument in the second term from "2x" to "x". See where that leads.

6. If tan(2x) = -24/7 , find the values of sin x and cos x

In what quadrant must 2x be? In what quadrant(s) could x then be? Using the double-angle formula, what value(s) do you obtain for tan(x)? What then could be the values of sin(x) and cos(x)?

Please be complete. Thank you!

Eliz.