Question

Is cos x sin x = 1 an identity?

Answer 1

No

Explanation:

An easy way to show that this is not an identity is to plug in `0` for `x`.

`cos(0)sin(0) = 0*1 = 0 != 1`

In fact, if we use the identity `sin(2x) = 2sin(x)cos(x)` we can show that there are no real values for which the questioned equality is true.

`cos(x)sin(x) = 1/2(2sin(x)cos(x))=sin(2x)/2`

Because `sin(2x)<=1` for all `x in RR` (for all real-valued `x`) that means that `cos(x)sin(x) <= 1/2` for all real `x`.

The more common trig identity which involves `1` is

`sin^2(x)+cos^2(x) = 1`

which is true for all `x`.

Answer 2

My answer;

Absolutely not

Explanation:

According to this

`cos x = 1/sinx= cscx`

\ I hope you get the point IT IS NOT TRUE FOR ALL VALUES OF X

So it is not an identity