Question

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

Answer 1

Answer:

cosec A =17 /15

I hope it will help you

Answer 2

If 15 cot A = 8 then the value of cosec A $=\frac{17}{15}$

Solution:

Given that 15 cot A = 8

We have to find the value of cosec A

From question,

15 cot A = 8

$\text { Hence cot } \mathrm{A}=\frac{8}{15}$ --- equation 1

The relation between cosec and cot is given through a trigonometric identity as follows:

$cosec^2 A - cot^ 2 A = 1$  

Substituting eqn 1 in eqn 2, we get

$Cosec^2 A -\left(\frac{8}{15}\right)^{2}=1$

$cosec^2 A = 1+\frac{64}{225}$

$=\frac{(225+64)}{225}=\frac{289}{225}$

By taking the square root on both sides

$cosec A =\sqrt{\frac{289}{225}}=\frac{17}{15}$

Hence the value of cosec A $= \frac{17}{15}$