simplify (sin^4 x - cos^4 x)/(sin x + cos x)

Question

tkhunny · Answer

Have you considered factoring?  Differences of Squares are wild!

luigi0210 · Answer

^That. Do you know the formula?

ranga · Answer

$$ a^2 - b^2 = (a-b)(a+b)$$$$ a^4 - b^4 = (a^2)^2 - (b^2)^2 = (a^2-b^2)(a^2+b^2) = (a-b)(a+b)(a^2+b^2)$$

anonymous · Answer

thank you all

anonymous · Answer

i will try ot hammer it out and if i cant ill be back!

anonymous · Answer

$$\sin ^{3}x+sinxcos ^{2}x+-cosxsin ^{2}x+-\cos ^{3}x$$

anonymous · Answer

$$
\frac{\sin ^4(x)-\cos ^4(x)}{\sin (x)+\cos (x)}=\\frac{(\sin (x)-\cos (x))
   (\sin (x)+\cos (x)) \left(\sin ^2(x)+\cos ^2(x)\right)}{\sin (x)+\cos
   (x)}=\\sin (x)-\cos (x)

$$

anonymous · Answer

We used the fact that
$$
\sin ^2(x)+\cos ^2(x)=1
$$

anonymous · Answer

ahhhh the cancellation and that pythagorean

anonymous · Answer

sinx-cosx, does that simplify?

anonymous · Answer

i guess thats it.  i tried to find a theorem for that but couldnt

anonymous · Answer

http://www.trans4mind.com/personal_development/mathematics/trigonometry/sumProductCosSin.htm