Question

find the value of cos(Cos^-1(sqrt2/2)-(pi/2)) a. 2 b. sqrt2 c. 2 x sqrt2 d. sqrt2/2

Answer 1

Answer:

d. $\frac{\sqrt{2}}{2}$

Step-by-step explanation:

1. The first step is calculate the inverse cosine function shown  in the exercise and substract this resul with π/2, as following:

$cos^{-1}(\frac{\sqrt{2}}{2})-(\pi/2)=(-\pi/4)$

2. Then you have that:

$cos(-\pi/4)=\frac{1}{\sqrt{2}}$

3. Simpliying:

$=\frac{\sqrt{2}}{2}$

Answer 2

answer : option d

$cos(cos^{-1}(\frac{\sqrt{2}}{2})-\frac{\pi}{2})$

LEts find $cos^{-1}(\frac{\sqrt{2}}{2})$

Lets assume $cos^{-1}(\frac{\sqrt{2}}{2})= x$

When we move cos^-1 to the other side then it becomes cos

$(\frac{\sqrt{2}}{2})= cos(x)$

So angle $x=\frac{\pi}{4}$

Hence , $cos^{-1}(\frac{\sqrt{2}}{2})=\frac{\pi}{4}$

We replace it in our problem

$cos(\frac{\pi}{4} -\frac{\pi}{2})$

Now take common denominator 4

$cos(\frac{\pi}{4} -\frac{\pi*2}{2*2})$

$cos(\frac{\pi-2\pi}{4})$

$cos(\frac{-\pi}{4})$

We know cos(-x) = cos(x)

$cos(\frac{-\pi}{4})=cos(\frac{\pi}{4})$

$cos(\frac{\pi}{4})=\frac{\sqrt{2}}{2}$