Evaluate (2sinx)(3sinx) (6cosx)(cosx)
2*3*6 sinx*sinx cosx*cosx
36 sin^2(x) cos^2(x)
or
9(2 sinx cosx)^2
9 sin^2(2x)
9/2 (1-cos(4x))
To evaluate the given expression, we can simplify it step by step.
First, let's simplify (2sin x)(3sin x):
(2sin x)(3sin x) = 6sin^2 x
Next, let's simplify (6cos x)(cos x):
(6cos x)(cos x) = 6cos^2 x
Now, we have:
6sin^2 x + 6cos^2 x
Since sin^2 x + cos^2 x = 1 (from the Pythagorean identity), we can substitute this value into the expression:
6sin^2 x + 6cos^2 x = 6(1) = 6
So, the final evaluation of the expression is 6.