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avatar+1124 

Hi friends,

 

I got stuck with this, and Google is not much help...please if someone would help me?

 

Determine without a calculator:

 

\({Cos72 \over{Sin24}}+{Sin72 \over{Cos24}}\)

 

This gives

 

\({Cos72Cos24+Sin72Sin24} \over{Sin24Cos24}\)

 

I do not see how to go further?..any help please?..Thank you kindly..

 Apr 18, 2023
 #1
avatar+397 
+1

Try looking through the list of trig identities that you should have.

 Apr 18, 2023
 #2
avatar+1124 
+1

Tiggsy,

 

Yes, I see,

The top would then be

 

\(Cos(72-24)\)

 

but the bottom part...I really do not see how to re-write that..

juriemagic  Apr 18, 2023
 #3
avatar+1124 
+1

I have here something that shows that (Sin(x)Cos(x)) can be written as \({1 \over2}(2SinxCosx)\)

How do they get to that?..please?

juriemagic  Apr 18, 2023
 #4
avatar+118616 
+1

You need to memorize

 

\(sin(A+B) = sinAcosB + cosAsinB\\ so\\ sin(2A)=sinAcosA+cosAsinA=2sinAcosA\)

 

It can be provben of course but you really need to memorize it.

 

 

so Sin24cos24 can be written as   0.5(2sin24cos24) = 0.5*sin48

 

 

Note: I have not looked at the whole question.

Melody  Apr 20, 2023

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