Trigonometric equations and inequalities

2010014905

Level: 
B
Identify the optimal first step convenient to solve the following trigonometric equation. Do not consider the step which is possible but does not help to solve the equation. tg2⁡x−2tg⁡x−3=0
substitution tg⁡x=y
tg⁡x(tg⁡x−2)=3
sin2⁡xcos2⁡x−2sin⁡xcos⁡x−3=0
tg⁡x−2=3−tg⁡x

2010014904

Level: 
B
Identify the optimal first step convenient to solve the following trigonometric equation. Do not consider the step which is possible but does not help to solve the equation. 3cos2⁡x=2sin⁡xcos⁡x
cos⁡x(3cos⁡x−2sin⁡x)=0
3cos⁡x=2sin⁡x
3(1−sin2⁡x)=2sin⁡xcos⁡x
3cos2⁡x2sin⁡xcos⁡x=1