How is 5/(sin5xcos5x) converted to 10/2sin10x?

Question

I am not sure if this is an Identity or not. I looked at the table of Identities and did not find this one. Someone Please Explain how this is Done. A mathematican wrote converted it. Please help.

Answer 1

This is NOT an identity.

sin(2x) = 2(sin x)(cos x)

In the same way

sin(10x) = 2(sin 5x)(cos 5x)

So we have:

10/(2sin10x) = 5/sin(10x)
= 5 / {2(sin 5x)(cos 5x)} ≠ 5 / {(sin 5x)(cos 5x)}

Notice the factor of 2 in the denominator on the left but not on the right. They differ by a factor of two and so are not an identity.

Answer 2

These are defiently not equal to each other. It is not an identity


I tried working it backwards
5 sin(10x)
10 sin(5x) cos(5x)

Theres no way 10 sin(5x) cos(5x) can equal 5/(sin5xcos5x)

Even by putting the original equations into a graphing calculator they are not equal

I would like to know about this "mathematican" that converted it.

Answer 3

remember that sin 2u=2 sin u cos u so that if you multiply your problem by 2/2 you get 10/(2 sin5x cos 5x). The denominator can be replaced by sin 10x so that the answer is 10/(sin 10x). I teach math at NMSU, there must be a mistake with the 2 in the denominator.

Answer 4

It's simply using the well known result that sin2A = 2sinAcosA

with A = 5x

Answer 5

Look up the double angle formula (sin2x=2sinxcosx)