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

[louie3006]

Homework Statement

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

 

[joeyar]

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??

 

[Mark44]

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.]