Homework Help: Math

Posted by Alycia on Friday, November 2, 2012 at 12:33pm.

I can only manipulate one side of the equation and the end result should be equal to the other side. please help.

((sinx + cosx)/(1 + tanx))^2 + ((sinx - cosx)/(1 - cotx))^2 = 1

Math - Steve, Friday, November 2, 2012 at 7:03pm
since there's only one side that needs manipulating, I'd pick the left side. :-)

since
1+tan = (sin+cos)/cos and
1-cot = (sin-cos)/sin

we have

[(sin+cos)*cos/(sin+cos)]^2 + [(sin-cos)*sin/(sin-cos)]^2

= sin^2+cos^2
= 1

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