Question

If sec A=17/15 then find the value of 2 sin A + tan A /2tan A - sin A​

Answer 1

Answer:

33/34

Step-by-step explanation:

secA=hypotenuse/base

by Pythagoras theorem find perpendicular

which will be 8 as 17,15,8 are Pythagorean triplet also

Sin A= 8/17

from given EQ __ 2×8/17 + 8/15 / 2×8/15 - 8/17

which will give 33/34

Answer 2

Concept:

Trigonometric ratios are the ratios of sides of the right-angle triangle.

Given:

sec A = 17 / 15

Find:

We are asked to find the value of (2 sin A + tan A ) / (2tan A - sin A​).

Solution:

We have,

sec A = 17 / 15

So,

Now,

Using Trigonometric ratios for SecA, TanA, and SinA.

i.e.

SecA = Hypotenuse / Base = 17 / 15

So,

We have to find out Perpendicular,

Using the Pythagoras theorem,

H² = P² + B²

Now,

Putting values,

17² = P² + 15²

We get,

289 = P² + 225

⇒

P² = 289 - 225

P² = 64

P =8,

Now,

Sin A = Perpendicular / Hypotenuse = 8 /17,

And,

TanA = Perpendicular / Base = 8 / 15,

So,

According to the question,

(2 sin A + tan A ) / (2tan A - sin A​)

Now,

Putting values,

i.e.

= ( 2 × 8/17 + 8/15) / ( 2 × 8/15 - 8/17)

= ( 16/17 + 8/15) / ( 16/15 - 8/17)

On simplifying we get,

= [(16 × 15 + 8 × 17)/255} / [(16 × 17 - 8 × 15)/255}

Now,

On simplifying we get,

= (376/255) / (152/255)

We get,

= 376/152

= 2.474

i.e.

(2 sin A + tan A ) / (2tan A - sin A​) = 2.474

Hence, the value of (2 sin A + tan A ) / (2tan A - sin A​) is 2.474.

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