Question

1-2cos²45.............​

Answer 1

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Answer 2

It appears that you have an expression $1 - 2\cos^2(45^\circ)$ that you want to simplify. Let's break it down step by step:

First, recall the trigonometric identity: $\cos^2(\theta) + \sin^2(\theta) = 1$, which holds true for any angle $\theta$.

In this case, since $45^\circ$ is a special angle where $\cos(45^\circ) = \sin(45^\circ) = \frac{\sqrt{2}}{2}$, we can substitute these values into the expression:

$1 - 2\cos^2(45^\circ) = 1 - 2\left(\frac{\sqrt{2}}{2}\right)^2$

Simplifying further:

$= 1 - 2 \times \frac{2}{4} = 1 - \frac{1}{2} = \frac{1}{2}$

So, $1 - 2\cos^2(45^\circ) = \frac{1}{2}$.