Question

Simplify the expression.

quantity cosecant of y plus cotangent of y times quantity cosecant of y minus cotangent of y divided by cosecant of y.

Answer 1

sin y

Explanation:

Start with the numerator

(csc y + cot y)(csc y - cot y)=csc²y - cot²y

cot²y = csc²y -1

replace cot²y with csc²y -1

csc²y - csc²y +1 =1

Then 1/csc y = sin y

Answer 2

siny is the answer.

Explanation:

The given expression is
`\frac{\text{(cosec y + cot y)(cosec y - cot y)}}{\text{cosec y}}`

We have to simplify this expression.

`\frac{\text{(cosec y + cot y)(cosec y - cot y)}}{\text{cosec y}}` =
`(cosec^(2)y-cot^(2)y)/(cosecy)` [Since (a-b) (a+b) = a²-b²]

Now we know (1 + cot² y) = cosec² y [identity]

The expression will become

`((1+cot^2y)-cot^2y)/(cosec y)`

=
`(1)/(cosec y)`

= Siny