Question

Let cos(2x)/cos(x)+sin(x) = 0 where 0° ≤ x ≤ 180°. What are the possible values for x?

Answer 1

C

Explanation:

`(cos2x)/(cos x+sin x) =(cos^2x-sin^2x)/(cos x+sin x) =((cos~x+sin~x)(cos~x-sin~x))/((cos~x+sin~x)) =cos~x-sin~x\\so~cos~x-sin~x=0\\divide ~by~cos~x\\1-tan~ x=0\\\\tan~x=1=tan ~45,tan (180+45)\\x=45^\circ,225^\circ`