how do you rewrite the expression to the 1st power of cosine by using power-reducing formulas? PLEASE AND THANK YOU :D
sin^2xcos^4x
To rewrite the expression sin^2(x)cos^4(x) to the 1st power of cosine using the power-reducing formulas, we can make use of the identity:
sin^2(x) = (1 - cos^2(x))
Let's break down the steps:
1. Start with the original expression: sin^2(x)cos^4(x).
2. Apply the power-reducing formula for sin^2(x): sin^2(x) = (1 - cos^2(x)).
3. Substitute sin^2(x) with (1 - cos^2(x)) in the original expression:
(1 - cos^2(x))cos^4(x).
4. Apply the Distributive Property to simplify:
cos^4(x) - cos^6(x).
Now, the expression sin^2(x)cos^4(x) has been rewritten to the 1st power of cosine using the power-reducing formula as cos^4(x) - cos^6(x).