prove this is right with identities:
(sin a)^4 + (cos a)^4 = 1 - 2 * (sin a)^2 * (cos a)^2

Question

prove  this is right with identities:
(sin a)^4 + (cos a)^4 = 1 - 2 * (sin a)^2 * (cos a)^2

anonymous · Answer

$$\sin ^{4}\alpha + \cos ^{4}\alpha = 1-2 \sin ^{2}\alpha \cos ^{2}\alpha$$

please help

hartnn · Answer

add and subtract  2 * (sin a)^2 * (cos a)^2 on left side :  
(sin a)^4 + (cos a)^4

hartnn · Answer

=[(sin a)^4 + (cos a)^4+2 * (sin a)^2 * (cos a)^2]-2 * (sin a)^2 * (cos a)^2
did you get what i did ?

anonymous · Answer

trying to... :) thank you...

hartnn · Answer

then notice that$ (\sin a)^4 =(\sin^2a)^2 $
same for cos^4 a
and that [(sin a)^4 + (cos a)^4+2 * (sin a)^2 * (cos a)^2] is of the form $x^2+y^2+2xy=(x+y)^2$

hartnn · Answer

are u getting any of this ? 
please interact and ask doubts....

anonymous · Answer

i'm writing it down and trying to get to eah of your steps by myself so it takes some times...thank u man :)

hartnn · Answer

good :) also think of next steps...

anonymous · Answer

okay, got it...
sin^2a + cos^2a = 1
1^2=1
you're awesome :) thanks alot

hartnn · Answer

welcome ^_^
thanks for the compliment :)