Question

1-2cos^2(pi/2+a) при a=pi/12

Answer 1

Вот посмотри , применила формулу и всё))

Answer 2

1-2sin^2a=1-2sin^2(p/12)=sin^2(p/12)+cos^2(p/12)-2sin^2(p/12)=cos^2(p/12)-sin^2(p/12=cosp/6=sqrt3/2

Answer 3

To evaluate the expression $1-2\cos^2\left(\frac{\pi}{2}+a\right)$ with $a=\frac{\pi}{12}$, we can substitute the value of $a$ into the expression and simplify it.

Let's begin by substituting $a=\frac{\pi}{12}$ into the expression:

$1-2\cos^2\left(\frac{\pi}{2}+\frac{\pi}{12}\right)$

Now, we can simplify the expression by using the trigonometric identity $\cos(\frac{\pi}{2}+\theta)=-\sin(\theta)$:

$1-2\sin^2\left(\frac{\pi}{12}\right)$

Next, we can use the trigonometric identity $\sin^2(\theta)=\frac{1-\cos(2\theta)}{2}$ to further simplify:

$1-2\left(\frac{1-\cos\left(\frac{\pi}{6}\right)}{2}\right)$

Now, let's simplify the expression inside the parentheses:

$1-2\left(\frac{1-\frac{\sqrt{3}}{2}}{2}\right)$

Simplifying further:

$1-\left(1-\frac{\sqrt{3}}{2}\right)$

$1-1+\frac{\sqrt{3}}{2}$

$\frac{\sqrt{3}}{2}$

Therefore, $1-2\cos^2\left(\frac{\pi}{2}+\frac{\pi}{12}\right) = \frac{\sqrt{3}}{2}$ when $a=\frac{\pi}{12}$.