Solve the equation cos x – sin x tan x + 1 = 0 for 0°≤x≤360°?

1 Answer
May 26, 2018

#x=pi/3# or #x=pi# or #x=5/3*pi#

Explanation:

Wrtiting your equation in the form
#cos(x)-sin(x)^2/cos(x)+1=0#
Using that
#sin(x)^2=1-cos(x)^2#
we obtain
#cos(x)-(1-cos(x)^2)/cos(x)+1=0#
Multiplying by #cos(x)ne 0#
we get
#2cos(x)^2+cos(x)-1=0#

solving this equation we get

#cos(x)=1/2#
or

#cos(x)=-1#
we get the Solutions above!