Make up your OWN identity. Start with a trigonometric expression, and apply substitutions and algebraic processes to create equivalent expressions.

Justify each step. Verify your identity graphically and algebraically.

I have already made up my own identity witch is

So an identity you can use is ... 1/4 sin^2 (2x) = sin^2(x) * (1-sin^2 (x))

Begin by thinking of sin and cosine. Cosine: cos(x) substituted with sqrt(1 - sin^2(x)) because of Pythagorean theorem

Then, consider the expression sin^2(x) * cos^2(x). This will become sin^2(x) * (1 - sin^2(x))

After that, factor the expression by taking out a sin^2(x) term: sin^2(x) * (1 - sin^2(x)) = sin^2(x) * (1 - sin^2(x))

Then, apply the double-angle identity sin(2x) = 2 * sin(x) * cos(x). We'll square both sides to get sin^2(2x) = 4 * sin^2(x) * cos^2(x)

Substitute sin^2(x) * (1 - sin^2(x)) from the earlier step into the double-angle identity: sin^2(2x) = 4 * sin^2(x) * (1 - sin^2(x))

Divide both sides by 4: (1/4) * sin^2(2x) = sin^2(x) * (1 - sin^2(x))

And that's what you have to do to get the identity

here is what I am expecting you to answer me the following identity is the teachers identity please dont copy just see so you can have an idea on how to work on it :

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