Use the power-reducing formulas to rewrite the expression in terms of the first power of the cosine.
[#1.] (sin^4x)(cos^4x)
[#2.] (sin^4x)(cos^2x)
(1-cos^2)(1-cos^2) (cos cos cos cos)
(1-cos)(1+cos)(1-cos)(1+cos)(cos)(cos)(cos)(cos)
the next one follows
To rewrite the expression in terms of the first power of cosine using the power-reducing formulas, we need to recall the following identities:
1. sin^2(x) = 1 - cos^2(x)
2. cos^2(x) = 1 - sin^2(x)
Now let's solve each expression step by step:
[#1.] (sin^4x)(cos^4x)
First, let's rewrite sin^4(x) using the power-reducing formula:
sin^4(x) = (sin^2(x))^2 = (1 - cos^2(x))^2
Now, let's rewrite cos^4(x) using the power-reducing formula:
cos^4(x) = (cos^2(x))^2 = (1 - sin^2(x))^2
Now, we can rewrite the expression in terms of the first power of cosine:
(sin^4x)(cos^4x) = [(1 - cos^2(x))^2][(1 - sin^2(x))^2]
[#2.] (sin^4x)(cos^2x)
First, let's rewrite sin^4(x) using the power-reducing formula:
sin^4(x) = (sin^2(x))^2 = (1 - cos^2(x))^2
Now, we can rewrite the expression in terms of the first power of cosine:
(sin^4x)(cos^2x) = [(1 - cos^2(x))^2](cos^2(x))
Note: In both cases, the expression cannot be further simplified using the power-reducing formulas. This is the final result when expressed in terms of the first power of cosine.