Re: -2cos(x) - sin(x) simplification?


crocostimpy@xxxxxxxxx wrote:
Can it be shown that

-2cos(x) - sin(x)

can be simplified to

[3cos^2(x)+1]^(1/2) ?


...I'm trying to prove that
(-2M/r^3)cos(x) + (-M/r^3)sin(x) = (M/r^3)[[3cos^2(x)+1]^(1/2)]

I've gotten so far as (M/r^3)(-2cos(x) - sin(x)), but am stuck there.
But that should mean that [[3cos^2(x)+1]^(1/2)] should equal (-2cos(x)
- sin(x)).

No, -2cos(x) - sin(x) = (3cos^2(x) + 1 + 2sin(2x))^(1/2) (provided you
take the appropriate sign for the square root).

.