Answer:
cosec A = [tex]\frac{17}{15}[/tex]
Step-by-step explanation:
We have,
15 cot A = 8
[tex]\implies cotA = \frac{8}{15}[/tex]
We know that,
cosec²A - cot²A = 1
⇒cosec²A = 1 + cot²A
Taking square root both sides, we get
[tex]\sqrt{cosec^2A} = \sqrt{1+cot^2A[/tex]
[tex]\implies cosec A = \sqrt{1+cot^2A}[/tex]
[tex]\implies cosec A = \sqrt{1+(\frac{8}{15})^2}[/tex]
[tex]\implies cosec A=\sqrt{1+\frac{64}{225}}=\sqrt{\frac{289}{225}}=\frac{17}{15}[/tex]
So, the value of cosec A is [tex]\frac{17}{15}[/tex].
