help please Ill give 5 points back to your test 3 grade for

help please?

I\'ll give 5 points back to your test #3 grade for an explanation of why it is NOT GENERALLY TRUE that For any positive integer n, cos^2 n (theta) + sin^2 n (theta) = 1.

Solution

Now, this result works ALWAYS only for n = 1

It works ALWAYS because when we plug in n = 1, we get :
cos^2t + sin^2t= 1

OR

cos^2t + sin^2t = 1^2, which as we know is the Pythagorean theorem applies to a triangle in the unit circle.

Granted that cos^2n(theta) + sin^2n(theta) = 1 works for when costheta = 1 and sintheta = 0
or when sintheta= 1 and costheta = 0.

But this happens only for very few values of theta.

Notice when n = 1 , cos^2t + sin^2t = 1 is ALWAYS true for EVERY value of theta.

So, the result is not generally true but it does work ALWAYS only when n = 1. And when n is not one, the result would work only for very few values of theta.

Thus, it is safe to say that this is not generally true.