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supernova1203
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Homework Statement
Prove the following identities
31c) sin([itex]\frac{\pi}{2}[/itex]+x)=cosx
Homework Equations
sin2x+cos2x=1
The Attempt at a Solution
The idea here is to prove the identity by making LS=RS
so here is what i have done, but I am not sure if it is the right way, since the book shows it went about it in a different way.
My method:
sin([itex]\frac{\pi}{2}[/itex]+x)=cosx
1+sinx=cosx
now we use the pythagreon identity
sin2x+cos2x=1
If we move the cos to the right side, we are left with sinx=-cosx
and we use another identity
cos-x=cosx
therefore LS=RS and we have proved the identity? Book method:sin([itex]\frac{\pi}{2}[/itex]+x)=cosx
LS=sin([itex]\frac{\pi}{2}[/itex]+x) RS=cosx
=sin[itex]\frac{\pi}{2}[/itex]cosx+cosx+cos[itex]\frac{\pi}{2}[/itex]sinx
=(1)cosx+(0)sinx
=cosx
LS=RS therefore sin([itex]\frac{\pi}{2}[/itex]+x)=cosx
Is my method correct? Also at the point where they do "=sin[itex]\frac{\pi}{2}[/itex]cosx+cosx+cos[itex]\frac{\pi}{2}[/itex]sinx" Are they still just dealing with LS only?
thanks!
Also if someone could please explain how the book got to the solution it did, what thought process does one have to use to get to the solution the way book did? Thanks
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