how can you condense these
cos^3x* cos2x^2
cos^3x+ cos2x^2
cos^3x- cos2x^2
Thanks a lot :)
To condense the given expressions, you can use trigonometric identities to simplify them. Here's how you can do it:
1. cos^3x * cos2x^2:
Using the identity cos(2x) = 2cos^2(x) - 1, we can rewrite the expression as:
cos^3x * (2cos^2(x) - 1)
Expanding this further:
2cos^5(x) - cos^3x
2. cos^3x + cos2x^2:
Since there is no trigonometric identity directly applicable here, we cannot simplify this expression further. Therefore, it remains as:
cos^3x + cos2x^2
3. cos^3x - cos2x^2:
Similar to the first expression, we can rewrite cos(2x) = 2cos^2(x) - 1:
cos^3x - (2cos^2(x) - 1)
Expanding this further:
cos^3x - 2cos^2(x) + 1
So, the condensed expressions are:
1. cos^3x * cos2x^2 = 2cos^5(x) - cos^3x
2. cos^3x + cos2x^2 = cos^3x + cos2x^2
3. cos^3x - cos2x^2 = cos^3x - 2cos^2(x) + 1