Question

if 15 cot A = 8, then find the value of cosec A​

Answer 1

Answer:

cosec A = $\frac{17}{15}$

Step-by-step explanation:

We have,

15 cot A = 8

$\implies cotA = \frac{8}{15}$

We know that,

  cosec²A - cot²A = 1

⇒cosec²A = 1 + cot²A

Taking square root both sides, we get

$\sqrt{cosec^2A} = \sqrt{1+cot^2A$

$\implies cosec A = \sqrt{1+cot^2A}$

$\implies cosec A = \sqrt{1+(\frac{8}{15})^2}$

$\implies cosec A=\sqrt{1+\frac{64}{225}}=\sqrt{\frac{289}{225}}=\frac{17}{15}$

So, the value of cosec A is $\frac{17}{15}$.