sine and cosine identity

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wendywoo

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Jun 12, 2011
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i can't figure this out. why is sin2x - cos2x = -cos2x ??? i thought according to the trig identity that sin2x + cos2x = 1. so shouldnt the answer be something else? like -1? i don't know where i'm going with this. is there a basic rule that i'm not grasping or?
 
wendywoo said:
i can't figure this out. why is sin2x - cos2x = -cos2x ??? i thought according to the trig identity that sin2x + cos2x = 1. so shouldnt the answer be something else? like -1? i don't know where i'm going with this. is there a basic rule that i'm not grasping or?
Click to expand...

cos**2 x - sin **2 x=cos 2x

cos(x+x)=cos**2 x - sin**2 x


remember cos (x+y)=cosx*cosy - sinx * siny
 
but how can i apply that identity rule to the problem. where did they even get a negative cos2x as an answer?! can you walk me through the steps please??
 
wendywoo said:
but how can i apply that identity rule to the problem. where did they even get a negative cos2x as an answer?! can you walk me through the steps please??
Click to expand...
It is well known that \(\displaystyle \cos(2x)=\cos^2(x)-\sin^2(x)\).
Multiply both sides by \(\displaystyle -1.\)
 
yes. it gives us -cos2x but i have no idea how i would've gotten that myself. and where did the -1 come from?
 
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