6^cos4x*6^cos6x=6^cos5x

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We can simplify this equation by using the property of exponents, which states that when multiplying two numbers with the same base, you can simply add the exponents.

So, we have:

6^(cos4x)*6^(cos6x) = 6^(cos4x + cos6x)

Since the equation we want to prove is 6^(cos5x), we need to show that cos4x + cos6x = cos5x.

We know that cos(4x) + cos(6x) = cos(5x) when cos(4x) = -1/2 and cos(6x) = -1/2.

Therefore, the equation 6^(cos4x)*6^(cos6x) = 6^(cos5x) is true when cos(4x) = -1/2 and cos(6x) = -1/2.

So, the equation 6^(cos4x)*6^(cos6x) = 6^(cos5x) holds true under the given conditions.