Question

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

Answer 1

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

Answer 2

Answer:

false

Step-by-step explanation: