Is cos x sin x = 1 an identity?

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Answer 1 · 2016-02-23T12:26:09

No

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 · 2016-02-23T12:27:11

My answer;

Absolutely not

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