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

C

Explanation:

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Answer 2

Answer: The correct option is (c).
`\csc x=(1)/(\sin x).`

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

`(\sin x+1)/(\sin x)=1+\csc x.`

We have

`(1+\sin x)/(\sin x)\\\\\\=(1)/(\sin x)+(\sin x)/(\sin x)\\\\\\=1+(1)/(\sin x).`

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

`1+(1)/(\sin x)=1+\csc x\\\\\\\Rightarrow (1)/(\sin x)=\csc x\\\\\\\Rightarrow \csc x=(1)/(\sin x).`

Thus, the required identity that we will use is

`\csc x=(1)/(\sin x).`

Option (c) is CORRECT.