Question 82694
simplify the expression: cscx(tan(-x))
{{{(1/(sinx))*((sin(-x))/(cos(-x)))}}}  Reciprocal identity
{{{(1/(sinx))*((-sinx)/(cosx))}}}  even an odd property
{{{-1/(cosx)}}}  cancel sinx
{{{-secx}}}  reciprocal identity
:
simplify the expression: cotxcos(3.14/2-x)
{{{cotx*cos(pi/2-x)}}}
{{{cotx*sinx}}}  complementary angles
{{{((cosx)/(sinx))*sinx}}}  reciprocal identity
{{{cosx}}}  cancel sinx
:
verify the identity: cos^4x-sin^4x=cos^2x-sin^2x
{{{(cos^2(x)+sin^2(x))(cos^2(x)-sin^2(x))}}}  factoring the difference of perfect squares
{{{1(cos^2(x)-sin^2(x))}}} pythagorean identity
{{{cos^2(x)-sin^2(x)=cos^2(x)-sin^2(x)}}}
:
These can actually be pretty fun once you've memorized all your identitities.  They're like puzzles.  Attack the more complicated side and simplify, it's much easier to break it down than to try to figure out how to build the simpler side into something more complicated.
Happy Calculating!!!!