Question

If cos A = 21/29, find the value of cosec A + tan A​

Answer 1

Answer:

1009/420

Step-by-step explanation:

Consider a ∆ABC in which angle B =90°.

Base (adjacent) = AB ,

Perp. (opposite side) = BC

and. Hyp. = AC.

Thus.

$\cos(a) = \frac{base}{hyp.} = \frac{ab}{ac} = \frac{21}{29}$

Let AB = 21k and AC = 29k.

Then, BC =

$\sqrt{ {ac}^{2} - {ab}^{2} } = \sqrt{( {29k)}^{2} - {(21k)}^{2} } = \sqrt{ {841k}^{2} - {441k}^{2} } = \sqrt{ {400k}^{2} } = 20k$

cosec A =

$\frac{hyp.}{perp.} = \frac{ac}{bc} = \frac{29k}{20k} = \frac{29}{20}$

and tan A =

$\frac{perp.}{base} = \frac{bc}{ab} = \frac{20k}{21k} = \frac{20}{21}$

Thus, cosec A + tan A =

$\frac{29}{20} + \frac{20}{21} = \frac{1009}{420}$

Here's your answer.

Hope it helps you.