SOLUTION: Solve the following equations give that 0 &#8804; x < 2&#960; a) {{{ cos^2 (x) -sin^2 (x) = -1 }}} b) {{{ 1 + sqrt (3) tan (2x) = 0 }}} --Need a refresher on how to so

Algebra ->  Equations -> SOLUTION: Solve the following equations give that 0 &#8804; x < 2&#960; a) {{{ cos^2 (x) -sin^2 (x) = -1 }}} b) {{{ 1 + sqrt (3) tan (2x) = 0 }}} --Need a refresher on how to so      Log On


   

Question 1094407: Solve the following equations give that 0 ≤ x < 2π
a) +cos%5E2+%28x%29+-sin%5E2+%28x%29+=+-1+

b) +1+%2B+sqrt+%283%29+tan+%282x%29+=+0+

--Need a refresher on how to solve these, I would appreciate any sort of help!
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the following equations give that 0 ≤ x < 2π
a) +cos%5E2+%28x%29+-sin%5E2+%28x%29+=+-1+
Sub (1 - sin^2) for cos^2
------
--> 1 - 2sin^2 = -1
sin^2 = 1
sin = 1, x = pi/2
sin = -1, x = 3pi/2
==================
Or use cos^2(x) - sin^2(x) = cos(2x)
cos(2x) = -1
2x = pi, 3pi
x = pi/2, 3pi/2
===========================================
b) +1+%2B+sqrt%283%29tan+%282x%29+=+0+
tan(2x) = -sqrt(3)/3
2x = 150 degs, 330 degs, 510 degs, 690 deg
x = 75, 165, 255, 345 degs
Convert to radians.