Question

Sin(-x)= -cos x for all values of x. True or false

Answer 1

The given expression :

`\sin (-x)=-\cos x` is a false expression i.e. it is not true for all the values of x.

Explanation:

We are asked to check whether the trignometric expression is true for all the values of x or not.

The expression is given by:

`\sin (-x)=-\cos (x)`

We consider x=0

Then on taking left hand side of the expression we have:

`\sin (-0)\\\\i.e.\\\\\sin (0)\\\\=0`

and the right hand side of the expression is:

`-\cos x\\\\i.e.\\\\-\cos 0\\\\i.e.\\\\-1`

i.e. we have:

`0=-1`

which is false.

Hence the statement is not true for all the values of x.

Answer 2

That's incorrect. The simplest way to show this is by evaluating the functions at a given point. Let's say x=0, then:

Sin(-x) = Sin(0) = 0

-cos x = -cos (0) = -1

Therefore, Sin(-x)≠-cos x.