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# Cos 72

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+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
+397
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Try looking through the list of trig identities that you should have.

Apr 18, 2023
#2
+1124
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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
+1124
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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
+118616
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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