Question

What basic trigonometric identity would you use to verify that sinx + 1/ sinx = 1+ cscx

Answer 1

$\frac{ \sin(x) + 1 }{ \sin(x) } = \frac{ \frac{1}{ \cos(x) } + 1 }{ \frac{1}{ \cos(x) } } = \cos(x) ( \frac{1}{ \cos(x) } + 1) = 1 + \cos(x) \\ \Rightarrow c. \cos(x) = \frac{1}{ \sin(x) }$

Answer 2

Answer:

C)  We use csc = $\frac{1}{sinx}$ to verify.

Step-by-step explanation:

Given : $\frac{sinx+ 1}{sinx}$ = 1 +csc x.

To find : What basic trigonometric identity would you use to verify.

Solution : We have given that  $\frac{sinx+ 1}{sinx}$ = 1 +csc x.

To  verify we need to show left hand side equal to right hand side.

For right hand side

1 +csc x  

By csc = $\frac{1}{sinx}$.

Plug the value  csc = $\frac{1}{sinx}$.

1 +  $\frac{1}{sinx}$.

Taking least common multiple

$\frac{sinx +1}{sinx}$ = left hand side.

We can see this is equal to left hand side

Hence , left hand side = right hand side.

Therefore, C)  We use csc = $\frac{1}{sinx}$ to verify.