Question

Solve the equation for all real values of x.
cos xtan x - 2 cos X=-1

Answer 1

Answer:

Step-by-step explanation:

cos x tan x-2 cos x=1

$cos x(\frac{sin x}{cos x} )-2 cos x=-1\\sin ~x-2 cos~x=-1\\squaring\\sin ^2x+4 cos^2x-4 sin x cos x=1\\4cos ^2x-4sin xcos x=1-sin ^2x=cos^2x\\3 cos ^2x-4sin xcos x=0\\cos x(3 cos x-4sin x)=0\\cos x=0=cos ((2n+1)\frac{\pi}{2})\\x=(2n+1)\frac{\pi}{2}\\where ~n~is~an~integer.$

or

$3cos x-4 sin x=0\\3cos x=4 sin x\\tan x=\frac{3}{4}=0.75\\x=tan^{-1}(0.75)=(180n+36.87 )^\circ\\where~ n~ is~ an~ integer.$