Question

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

Answer 1

Solution :

Here, we'll use some trigonometric formulas.

• 15tanθ = 8

=> tanθ = 8/15

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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