Answer:
Option c. is correct.
Step-by-step explanation:
if [tex]sin\theta[/tex] < 0 means values of [tex]sin\theta[/tex] will be negative.
For [tex]tan\theta =\frac{sin\theta }{cos\theta }[/tex] > 0 means positive value of [tex]tan\theta[/tex]
values of [tex]sin\theta[/tex] and [tex]cos\theta[/tex] both should be either > 0 or < 0 for the poitive values of [tex]tan\theta[/tex]. If any one, sine or cosine is negative then [tex]tan\theta[/tex] will be < 0
We know that for the condition [tex]tan\theta > 0[/tex] and [tex]sin\theta[/tex] < 0 value of [tex]cos\theta[/tex] should be negative.
Therefore, [tex]\theta[/tex] should lie in 3rd quadrant where [tex]sin\theta[/tex] and [tex]cos\theta[/tex] both are negative.
Option C. 3rd option is correct.
