Question

Factor the left hand side of the identity

2cos^2(x)*sin^2(x)+sin^4(x)=1-cos^4(x)

Answer 1

Since it's an identity I can assume it's the same as the right side and factor that...

Answer 2

factor out a sin^2
\[sin^\{\2\}\ x \(\2cos^\{\2\}\ x \+\ sin^\{\2\}\ x)\\]
use pythagorean identity: sin^2 = 1-cos^2
\[(\1\-cos^\{\2\}x)\(\2cos^\{\2\}x \+\1\-cos^\{\2\}x)\\]
\[(\1\-cos^\{\2\}x)\(\1\+\ cos^\{\2\}\ x)\\]

Answer 3

hopefully the Latex is showing ok...its not working on my end :|

Answer 4

do u write this as
\(sin^2(x)[2cos^2x+sin^2]\) in ur first equation @dumbcow ?

Answer 5

yes

Answer 6

ok ! i gt it :)

Answer 7

factor out a sin^2\[\sin^{2} x (2\cos^{2} x + \sin^{2} x)\]use Pythagorean identity:-\[\sin^2 = 1-\cos^2\]\[(1-\cos^{2}x)(2\cos^{2}x +1-\cos^{2}x)\]\[(1-\cos^{2}x)(1+ \cos^{2}x)\] clear form of @dumbcow 's reply :)

Answer 8

gt it @biogirl ??

Answer 9

yes thank you

Answer 10

you are welcome from @dumbcow :)

Answer 11

\[\huge \color{red}{\text{Welcome to Open Study}}\ddot\smile\]