# Verify the identity: (Picture) Thanks for your time

*print*Print*list*Cite

### 2 Answers

There are often multiple ways to verify trig identities. Here is an alternative way to approach the problem. Here is another option:

`(cos^3x*sec^2x+tanx*sinx)/(cotx*sinx)*cscx`

First substitute for a couple of the reciprocal and quotient identities:

`(cos^3x*(1/(cos^2x))+(sinx/cosx)*sinx)/(cosx/sinx*sinx)*cscx`

Then we can cancel and combine the smaller fractions:

`(cosx+(sin^2x)/cosx)/cosx*cscx`

We can then divide each term in the numerator by the denominator:

`(cosx/cosx+((sin^2x)/cosx)/cosx)*cscx`

We can then simplify each of these fractions:

`(1+(sin^2x)/(cos^2x))*cscx`

We can then use one of the quotient identities again:

`(1+tan^2x)*cscx`

And finally we will use one of the Pythagorean identities:

`sec^2x*cscx`

`cscx*sec^2x`

### User Comments

**See the attachment for the solution.**