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sabika13
 2 years ago
how do prove this identity: sin^4x cos^4x=12cos^2x
sabika13
 2 years ago
how do prove this identity: sin^4x cos^4x=12cos^2x

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zordoloom
 2 years ago
Best ResponseYou've already chosen the best response.1Do you still need help?

sabika13
 2 years ago
Best ResponseYou've already chosen the best response.0RS: (sin^2x+cos^2x)2cos^2x sin^2xcos^2x Thats how much i can simplify right side..

zordoloom
 2 years ago
Best ResponseYou've already chosen the best response.1So here is how I proved it:

zordoloom
 2 years ago
Best ResponseYou've already chosen the best response.1So, change sinx^4 to (1cosx^2)^2

zordoloom
 2 years ago
Best ResponseYou've already chosen the best response.1You can expand that and you get 12cosx^2+cosx^4cosx^4=12cosx^2

zordoloom
 2 years ago
Best ResponseYou've already chosen the best response.1Do you follow so far?

zordoloom
 2 years ago
Best ResponseYou've already chosen the best response.1@sabika13 Should I continue?

zordoloom
 2 years ago
Best ResponseYou've already chosen the best response.1When you simplify 12cosx^2+cosx^4cosx^4=12cosx^2, the left side becomes 12cosx^2=12cosx^2

zordoloom
 2 years ago
Best ResponseYou've already chosen the best response.1That proves the identity.

zordoloom
 2 years ago
Best ResponseYou've already chosen the best response.1Normally, when you prove an identity, you work on one side. In this problem I worked on the left side.

sabika13
 2 years ago
Best ResponseYou've already chosen the best response.0wait how does (12cosx^2)^2=12cos^2+cosx^4?

zordoloom
 2 years ago
Best ResponseYou've already chosen the best response.1To summarize it: You have sin(x)^4cos(x)^4=12cos(x)^2 change sin(x)^4 >(1cos(x)^2)^2 You have: (1cos(x)^2)^2cos(x)^4=12cos(x)^2 Then expand (1cos(x)^2)^2 on the left side. You get 12cos(x)^2+cos(x)^4cos(x)^4=12cos(x)^2

zordoloom
 2 years ago
Best ResponseYou've already chosen the best response.1Then the: cos(x)^4cos(x)^4 cancel out.

sabika13
 2 years ago
Best ResponseYou've already chosen the best response.0im having problems expanding (1cos^2x)^2 shouldnt it be: 1cos^4x :S

zordoloom
 2 years ago
Best ResponseYou've already chosen the best response.1So, (1cos^2x)(1cos^2x). Just foil out.

sabika13
 2 years ago
Best ResponseYou've already chosen the best response.0ohhh okay, but why is it not: (1cos^2x)(1+cos^2x)

zordoloom
 2 years ago
Best ResponseYou've already chosen the best response.1It's squared. It's not a difference of squares.

sabika13
 2 years ago
Best ResponseYou've already chosen the best response.0ohh i think i get it...

zordoloom
 2 years ago
Best ResponseYou've already chosen the best response.1Any number, or equation squared is the same as it times by itself. Example (6)^2= (6)*(6) or (3x2)^2= (3x2)(3x2). Do you get the point?

zordoloom
 2 years ago
Best ResponseYou've already chosen the best response.1You don't change the signs inside the equation.

sabika13
 2 years ago
Best ResponseYou've already chosen the best response.0yeah so whats difference of squares then (if you dont mind me asking)

zordoloom
 2 years ago
Best ResponseYou've already chosen the best response.1example x^24. When you factor it, you get (x2)(x+2). It's a^2b^2

sabika13
 2 years ago
Best ResponseYou've already chosen the best response.0ohhh thankkyou!!you helped me fix a very big misconception inmy head ;P
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