Sin(-x)=-cosx for all values of x.

Question

asked Aug 23, 2020 221k views

2 Answers

Price · Answer 1 · 2020-08-28T21:15:07+0000

The given statement :

$\sin (-x)=-\cos x$ is a False statement.

We are given a statement as:

$\sin (-x)=-\cos x$ for all the values of x.

But this expression is not correct.

for example if we take x=0

then we have:

$\sin (0)=-\cos (0)\\\\i.e.\\\\0=-1$

which is incorrect.

Also, when
$x=(\pi)/(2)$

we have:

$\sin (-(\pi)/(2))=-\cos ((\pi)/(2))\\\\i.e.\\\\-\sin ((\pi)/(2))=-\cos ((\pi)/(2))\\\\i.e.\\\\-1=0$

which is again a false identity.

Hence, we get that the given statement is False.