Answer:
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.
The given expression :
[tex]\sin (-x)=-\cos x[/tex] is a false expression i.e. it is not true for all the values of x.
We are asked to check whether the trignometric expression is true for all the values of x or not.
The expression is given by:
[tex]\sin (-x)=-\cos (x)[/tex]
We consider x=0
Then on taking left hand side of the expression we have:
[tex]\sin (-0)\\\\i.e.\\\\\sin (0)\\\\=0[/tex]
and the right hand side of the expression is:
[tex]-\cos x\\\\i.e.\\\\-\cos 0\\\\i.e.\\\\-1[/tex]
i.e. we have:
[tex]0=-1[/tex]
which is false.
Hence the statement is not true for all the values of x.
