Question

Cos^-1(-x)=-Cos^-1x for -1<x<1 TRUE OR FALSE?

Answer 1

false

Explanation:

Answer 2

We are given

`cos^(-1)(-x)=-cos^(-1)(x)`

Firstly, we will simplify left side

and we will check whether it is equal to right side

Left side:

Let's assume y left side expression

`y=cos^(-1)(-x)`

now, we can take cos on both sides

`cos(y)=cos(cos^(-1)(-x))`

we can simplify it

`cos(y)=-x`

Right side:

Let's assume y left side expression

`y=-cos^(-1)(x)`

Multiply both sides by -1

`-y=cos^(-1)(x)`

now, we can take cos on both sides

`cos(-y)=cos(cos^(-1)(x))`

we can simplify it

`cos(-y)=x`

`cos(y)=x`

we can see that

both sides cos(y) value is different

so, this is FALSE.........Answer