Question

If sinθ=-5/13 and 180°<θ<270°, then find 5cot²θ + 12tanθ + 13cosecθ.

Answer 1

The angle θis in 3rd quadrant where only tanθ is positive while other trigonometric ratios are all negative.

Now, sinθ=5/13⇒cosθ=−√(1−sin2θ)=−√(1−25/169)=−√144/169=−12/13⇒tanθ=+5/12

cotθ=+12/5. cosecθ=−1/sinθ=−13/5

So, 5cot^2θ+12tanθ+13cosecθ=5∗144/25+12∗5/12+13∗−13/5

=144/5+5−169/5

=0