if P(s) lies in the second quadrant, then (cos s) (tan s ) > 0

Question

trigonometry

Answer 1

tan(s) can be written as sin(s)/cos(s)

 

Therefore cos(s) * tan(s) = cos(s) * sin(s)/cos(s) 

 

which is equivalent to cos(s)/cos(s) * sin(s) or just sin(s)

 

In the domain pi/2 to pi (2nd quadrant), the value of sin(pi/2) = 1 and value of sin(pi) = 0

 

so sin(s) > 0