Find all solutions of the equations in the interval 0 2pi Us

Find all solutions of the equations in the interval (0, 2pi). Use exact radian values where possible. Use trig substitutions when necessary. Remember, not all problems may require this strategy.

4. cosx + sinxtanx = 0

5. sec2x - 3tanx = 5

Solution

4) cosx + sinx*tanx = 0

cosx + sinx*sinx/cosx = 0 ====> (cos^2 x + sin^2 x)/cos x = 0 =======> 1/cosx = 0

=====> x = not defined

5) sec²x - 3tanx = 5

1 + tan²x - 3tanx = 5

   tan²x - 3tanx - 4 = 0

tanx = 4 ======> x = 76, 256 degrees = 1.326, 4.468 radians

  tanx = -1 ======> x = -45 = 315 , 135 degree ======> 5.5, 2.356 radians