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If sinθ=-5/13 and 180°

Answer»

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


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