Help proving trig identities

supersam1130 · **Joined:** Thu, 5 Apr 2012 20:56:32 UTC **Posts:** 7

Hello. I need some help solving these trig identities. It's really important that I understand HOW the answers are reached. The teacher said the assignment would be just like what we did in class, but i think he lied..

sec^4(x)-tan^4(x)=sec^2(x)+tan^2(x)

For this problem, the fourth power confuses me, would I take a squareroot of the first side to bring it down to a square?

mathematic · **Joined:** Fri, 1 Jul 2011 01:17:26 UTC **Posts:** 322

supersam1130 wrote:

Hello. I need some help solving these trig identities. It's really important that I understand HOW the answers are reached. The teacher said the assignment would be just like what we did in class, but i think he lied..

sec^4(x)-tan^4(x)=sec^2(x)+tan^2(x)

For this problem, the fourth power confuses me, would I take a squareroot of the first side to bring it down to a square?

You need to use sec^4 - tan^4 = (sec^2 + tan^2)(sec^2 - tan^2). The rest should be very easy.

supersam1130 · **Joined:** Thu, 5 Apr 2012 20:56:32 UTC **Posts:** 7

Thank you!

Shadow · **Posted:** Thu, 5 Apr 2012 22:07:25 UTC

supersam1130 wrote:

Thank you! Could you tell me why, when you break down sec^4 - tan^4 it becomes (sec^2 + tan^2)(sec^2 - tan^2)? I don't understand why there is a sec and a tan in each of the parenthesis

You learned back in algebra 1 or 2 that (x+y)(x-y)=x^2-y^2

supersam1130 · **Joined:** Thu, 5 Apr 2012 20:56:32 UTC **Posts:** 7

I realized that a second after I posted that reply, then I tried changing it... haha..
These problems scare me so much I get nervous and over think them. I really appreciate your help. <3

S.O.S. Mathematics CyberBoard

Help proving trig identities

Who is online