Verify that secX(tanX+cotX)=cscX/cos^2X

I've been bonking my head all day!! If someone could help me with this I'd greatly appreciate it.

I haven't done this in forever. Bear with me.

Work with the left side (or right because both works, but for my purposes, I'm just going to use the left), and turn secX, tanX, and cotX into terms you already know. We know that secX = 1/cosX, tanX=sinX/cosX, and cotX = cosX/sinX

If you don't, you must remember this and not blow it off because it will come back to haunt you. Treat it like it's your multiplication table again and get that hammered into your head.

1/cosX(sinX/cosX+cosX/sinX)

Multiply:

sinX/cos^2X + 1/sinX

And it turns into:

sin^2X+cos^2X/cos^2X*sinX = 1/cos^2X*sinX

1/cos^2X*1/sinX

1/cosX*csc/1 = cscX/cos^2X

you did that so quickly... are you sure it's right??

These trigonometric identities? I can verify any of them in a matter of minutes. I might have been wrong because I typed it rather quickly. Is there something you find that's incorrect?

Okay.. thanks. You are a genius!

Not really. If your algebra skills are strong, this comes easily.