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

Question

asked Oct 13, 2020 31.0k views

2 Answers

Rhldr · Answer 1 · 2020-10-14T15:44:41+0000

The given expression :

$\sin (-x)=-\cos x$ 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:

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

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.

Richard Vanbergen · Answer 2 · 2020-10-20T10:52:36+0000

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.