Question

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

Answer 1

cosec A =
`(17)/(15)`

Explanation:

We have,

15 cot A = 8

`\implies cotA = (8)/(15)`

We know that,

cosec²A - cot²A = 1

⇒cosec²A = 1 + cot²A

Taking square root both sides, we get

`√(cosec^2A) = \sqrt{1+cot^2A`

`\implies cosec A = √(1+cot^2A)`

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

`\implies cosec A=\sqrt{1+(64)/(225)}=\sqrt{(289)/(225)}=(17)/(15)`

So, the value of cosec A is
`(17)/(15)`.