Solve the equation by factoring Let k be any integer Round t

Solve the equation by factoring. Let k be any integer. Round terms to three decimal places.

2 cos() tan() + tan() = 1 + 2 cos()

Thank you!

Solution

2 cos theta tan theta + tan theta =1 + 2 cos theta

tan theta(2cos theta +1)=2 cos theta +1

(2 cos theta +1)(tan theta-1)=0

cos theta=-1/2, tan theta=1

theta= 3pi/4,5pi/4,pi/4