Prove that sec2x=(1/2)(secx)(cscx)

Question

anonymous · Answer

How far have you gotten?

anonymous · Answer

According to my calculations, that statement is not true.

anonymous · Answer

are you sure??

LS= 1/cos2x

RS= 1/2sinxcosx

anonymous · Answer

Wait. Is the right side (1/2)(secx)(cscx) or 1/2sinxcosx

anonymous · Answer

okokok its sec2x=1/2(secx)(cscx)

anonymous · Answer

so RS i did 1/2(1/cosx)(1/sinx)

anonymous · Answer

In the end, that will simplify to sin(2x) = cos(2x), which can only equal at a specific value of x.

jim_thompson5910 · Answer

If you graph the two sides separately as different functions, you'll notice they do not line up perfectly (see attached image).

So that visually confirms this equation is not an identity.

paxpolaris · Answer

maybe it shoould read:$$ \color{red}\csc2x=\frac12\sec x \cdot \csc x$$

anonymous · Answer

ok thank you all!

jim_thompson5910 · Answer

If PaxPolaris is correct with that equation, then it is an identity because graphing the two has them lining up perfectly. One graph is perfectly on top of the other as you can see in the attached gif file.

jim_thompson5910 · Answer

Of course, this isn't proof your teacher is looking for, but it's handy to have visual confirmation.