cos4x^2 + sin4x^2?
Is it 4 or 1?
cos²(x) + sin²(x) = 1
you can substitute x for any other angle, such as 4x, the identity still holds.
To simplify the expression cos(4x^2) + sin(4x^2), we need to use trigonometric identities. Let's break it down step by step.
Step 1: Rewrite the expression using the double-angle identities.
cos(4x^2) + sin(4x^2) = 2cos^2(2x^2) - 1 + 2sin(2x^2)cos(2x^2)
Step 2: Apply the Pythagorean identity to simplify the expression.
Recall that the Pythagorean identity states that cos^2(x) + sin^2(x) = 1.
Since we have cos^2 in the expression, we can rewrite sin^2(x) as 1 - cos^2(x).
sin(2x^2) = √(1 - cos^2(2x^2))
Step 3: Substitute the rewritten expression into the original expression.
cos(4x^2) + sin(4x^2) = 2cos^2(2x^2) - 1 + 2sin(2x^2)cos(2x^2)
= 2cos^2(2x^2) - 1 + 2√(1 - cos^2(2x^2))cos(2x^2)
Now, the expression is simplified as much as possible given the available information. If you have specific values for x, you can further simplify by substituting them into the equation.