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 : option d

`cos(cos^(-1)((√(2))/(2))-(\pi)/(2))`

LEts find
`cos^(-1)((√(2))/(2))`

Lets assume
`cos^(-1)((√(2))/(2))= x`

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

`((√(2))/(2))= cos(x)`

So angle
`x=(\pi)/(4)`

Hence ,
`cos^(-1)((√(2))/(2))=(\pi)/(4)`

We replace it in our problem

`cos((\pi)/(4) -(\pi)/(2))`

Now take common denominator 4

`cos((\pi)/(4) -(\pi*2)/(2*2))`

`cos((\pi-2\pi)/(4))`

`cos((-\pi)/(4))`

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

`cos((-\pi)/(4))=cos((\pi)/(4))`

`cos((\pi)/(4))=(√(2))/(2)`

Answer 2

d.
`(√(2))/(2)`

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)((√(2))/(2))-(\pi/2)=(-\pi/4)`

2. Then you have that:

`cos(-\pi/4)=(1)/(√(2))`

3. Simpliying:

`=(√(2))/(2)`