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Prove the identity: `cos^4x -sin^4x=1+2sin^2 x` ``
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Add `sin^4 x` both sides.
`cos^4 x=1+2sin^2 x+sin^4 x`
Use the formula: `a^2+2ab+b^2=(a+b)^2`
Compare `1+2sin^2 x+sin^4 x` and `a^2+2ab+b^2` and notice that a=1 and b=sin^2 x
Restrict `1+2sin^2 x+sin^4 x` using the formula.
`1+2sin^2 x+sin^4 x=(1+sin^2 x)^2`
Use the basic formula of trigonometry.
`sin^2 x+cos^2 x=1 =gtsin ^2 x = 1 - cos^2 x`
`(1+sin^2 x)^2 = (2-cos^2 x)^2`
If you expand the square `(2-cos^2 x)^2` you will obtain the result:
`(2-cos^2 x)^2 = 4 - 4cos^2 x + cos^4 x`
Notice that you did not get an identity.
ANSWER: `cos^4 x - sin ^4 x!= 1+2sin^2 x.`
The expression is not identity.
Posted by sciencesolve on November 22, 2011 at 8:44 PM (Answer #1)
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