Is cos x sin x = 1 an identity?

2 Answers
Feb 23, 2016

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.

Feb 23, 2016

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