1.

If 15 tan theta =8 find the values of cos theta and cosec theta​

Answer»

Solution :

Here, we'll use some TRIGONOMETRIC formulas.

  • 15tanθ = 8

=> tanθ = 8/15

----------------------------

As we KNOW that :

  • tanθ = P/B

Here, P refers to 8 and B refers to 15

Put k in the ratio

  • P = 8k
  • B = 15k

H² = P² + B² [ PYTHAGORAS theorem ]

Put the values -

⠀⠀⠀⠀=> H² = (8k)² + (15k)²

⠀⠀⠀⠀=> H² = 64k² + 225k²

⠀⠀⠀⠀=> H² = 289k²

⠀⠀⠀⠀=> H = √289k²

⠀⠀⠀⠀=> H = 17k units

Now,

  • cosθ = B/H = 15k/17k = 15/17
  • cosecθ = H/P = 17k/8k = 17/8

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More to know :

  • sinθ = P/H
  • cosθ = B/H
  • tanθ = P/B
  • cosecθ = H/P
  • secθ = H/B
  • cotθ = B/P

Where :

  • P denotes Perpendicular
  • B denotes BASE
  • H denotes Hypotenuse


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