Question

if sin theta =-5/13 and theta us in the third quadrant , then prove that 5cotsquare theta + 12tan theta + 13cosec theta=0​

Answer 1

Answer:

0

Step-by-step explanation:

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Answer 2

Given:

sinθ = −5/13 and θ is in the third quadrant.

To Prove:

5cot^2θ+12tanθ+13cosecθ=0.

Proof:

In 3rd quadrant, only tanθ and cotθ are positive.

sin^2θ + cos^2θ = 1

=> cos^2θ = 1 - (-5/13)^2

=> cos^2θ = (12/13)^2

=> cosθ = -12/13 (As cosθ is negative in 3rd quadrant)

• tanθ = sinθ/cosθ = 5/12
• cotθ = 1/tanθ = 12/5
• cosecθ = 1/sinθ = -13/5

5cot^2θ+12tanθ+13cosecθ

= 5(12/5)^2 + 12(5/12) + 13(-13/5)

= 144/5 + 5 - 169/5

= -25/5 + 5

= -5 + 5

= 0

Hence, it is proved.

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