Question

What basic trigonometric identity would you use to verify that sin x +1/ sin x=1 +csc x
a.sinx=cos x tan x
b.cos^2 x+ sin^2 x=1
c. csc x=1/ sin
d.1+cot^2x=csc^2x

Answer 1

Answer:  The correct option is (c). $\csc x=\dfrac{1}{\sin x}.$

Step-by-step explanation:  We are given to select the correct basic identity that we will use to verify the following:

$\dfrac{\sin x+1}{\sin x}=1+\csc x.$

We have

$\dfrac{1+\sin x}{\sin x}\\\\\\=\dfrac{1}{\sin x}+\dfrac{\sin x}{\sin x}\\\\\\=1+\dfrac{1}{\sin x}.$

In order to verify the given trigonometric equation, we must have

$1+\dfrac{1}{\sin x}=1+\csc x\\\\\\\Rightarrow \dfrac{1}{\sin x}=\csc x\\\\\\\Rightarrow \csc x=\dfrac{1}{\sin x}.$

Thus, the required identity that we will use is

$\csc x=\dfrac{1}{\sin x}.$

Option (c) is CORRECT.

Answer 2

Answer:

C

Step-by-step explanation:

Edge2021