Math, asked by mohanrajs7705, 7 months ago

If sin A = 5/13. Find the value of 5tan²A + 4 CotA.

Answers

Answered by DrNykterstein
8

Given that,

  • sin A = 5/13

We have to find the value of 5tan²A + 4 cotA

We know,

⇒ sin A = Perpendicular / Hypotenuse

⇒ 5/13 = Perpendicular / Hypotenuse

Therefore, comparing both sides, we have

  • Hypotenuse = 13k
  • Perpendicular = 5k

Imaging this in a right angled triangle.

I have attached the diagram.

Using the Pythagoras theorem in the triangle, we have

⇒ Hypotenuse² = Perpendicular² + Base²

⇒ (13k)² = (5k)² + Base²

⇒ 169k² - 25k² = Base²

⇒ 144k² = Base²

Base = 12k

Now, that we have perpendicular, base and hypotenuse, we can the required trigonometric ratios,

⇒ tan A = Perpendicular / Base

⇒ tan A = 5k / 12k

tan A = 5 / 12

Also,

⇒ cot A = 1 / tan A

⇒ cot A = 1 / (5/12)

cot A = 12 / 5

Now, Substituting the values of tan A and cot A in the given expression,

⇒ 5tan²A + 4cotA

⇒ 5(5/12)² + 4(12/5)

⇒ 125/144 + 48/5

⇒ (625 + 6912) / 720

⇒ 7537 / 720

Hence, The value of the given expression is 7537/720

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Answered by Anonymous
31

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