Question

how does cos(pi/4)^2 becomes (1/square root of 2)^2?

Answer 1

[AI-generated answer — Bot GPT 3.5]

Let's simplify the expression step by step:

Start with cos(pi/4)^2
cos(pi/4) is equal to 1/sqrt(2) (This is a well-known value)
So, cos(pi/4)^2 = (1/sqrt(2))^2
To square a fraction, we square the numerator and denominator separately:
(1^2)/(sqrt(2)^2)
Simplifying further, (1^2) is equal to 1 and (sqrt(2)^2) is equal to 2:
1/2
Thus, cos(pi/4)^2 is equal to (1/sqrt(2))^2 = 1/2.