Question

SIMPLIFY: csc(x) sin(x) + sin(x) − csc(x) ?

Answer 1

See below

Explanation:

`csc(x) sin(x) + sin(x) − csc(x)`

Reciprocal identity: `cscx=1/sinx`
`1/cancelsinx* cancelsin(x) + sin(x) − 1/sinx`

`1+sin^2x/sinx-1/sinx`

`1+(sin^2x-1)/sinx`

Use pythagorean identity: `sin^2x+cos^2x=1`

`1+(sin^2x-(sin^2x+cos^2x))/sinx`

`1-cos^2x/sinx`

`1-cosx/sinx*cosx`

Use quotient identity: `cosx/sinx=cotx`
`1-cotxcosx`