Verifying Identity: sinX(1-2cos^2x+cos^4x)=sin^5x

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The equation sinX(1-2cos^2x+cos^4x)=sin^5x raises questions about the capitalization of "sinX" versus "sinx." Assuming the capitalization is accidental, dividing both sides by sinx simplifies the equation to 1 - 2cos^2x + cos^4x = sin^4x. The discussion suggests that the left side can be factorized, hinting at a potential path to proving the identity. Additionally, it emphasizes the importance of parentheses for clarity in the original equation. The conversation revolves around verifying the identity through algebraic manipulation.
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Homework Statement


sinX(1-2cos^2x+cos^4x)=sin^5x
 
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On the left hand side of the equation, you have sinX and on the right sinx.

Is this capitalisation deliberate, or accidental.

Assuming it's accidental, your first step would be to divide both sides by sinx.

This gives

1 - 2cos^2x + cos^4x = sin^4x.

Can you do anything with that?

Clue: Can the left hand side be factorised??
 
Last edited:
louie3006 said:

Homework Statement


sinX(1-2cos^2x+cos^4x)=sin^5x
Assuming that you need to prove that this is an identity, you can work with one side to show that it is equal to the other side, or work with each side separately to get to expressions that are identical.

The left side is sin(x) (1 - cos^2(x))^2 [Parentheses would be very helpful in your original equation.]
 

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