Question

13. Given : 17 cos 0 = 15;
find the value of tan 0 + 2 sec O.

Answer 1

Answer:

14/5

Step-by-step explanation:

17 cos ∆ = 15 .....(∆ is theta)

cos ∆ = 15/17.

we know,

sin²∆ + cos²∆ = 1 ...(identity)

sin²∆ = 1 - cos²∆

sin²∆ = 1 - (225/289)

sin²∆ = (289 - 225) / 289 ...(taking LCM)

sin²∆ = 64/289

sin∆ = 8/17 ....(square root)

Now,

tan∆ = sin∆ / cos∆

$tan( \alpha ) = \frac{8}{17} \div \frac{15}{17}$

therefore,

tan ∆ = 8/15

and sec ∆ = 1/cos∆ = 17/15

therefore,

tan∆ + 2sec∆

==> 8/15 + 2(17/15)

==> 8/15 + 34/15 = 42/15

==> 14/5

Therefore the Value of tan∆ + 2sec∆ = (14/5)

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