Help please, Stuck with these question

hint for the first:

on the left side multiply the first term with (sec-tan) / (sec-tan) and the second term with (sec+tan) / (sec+tan), then you can combine the two terms with (sec+tan)(sec-tan)=sec^2 - tan^2 below the line
now use the identity sec=sqrt(1+tan^2), ie sec^2=1+tan^2 and when you put it in you will have 1+tan^2-tan^2 ie just 1 below the line

hint for the 2nd one:

the left hand side is the difference of 2 cubes, there is a formula for that:



use that to transform the left hand side and I think the rest will become obvious.

This post was edited by Azrad on Aug 18 2013 04:17am

3rd one is a beast IMO:

using the right hand side:

• expand it
• convert everything to sin and cos
• group the parts with sin together, and the parts with cos together
• in each "group" get a common denominator and add
• convert 1-sin^2 to cos^2, and 1-cos^2 to sin^2
• convert everything into tangent and cotangent

yuck! (I bet there is a more elegant way to do it, but I don't see it).

This post was edited by Azrad on Aug 18 2013 04:32am