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In ∆ABC, if sin A = and tan A = , then what is cos A?

 Nov 1, 2016
 #1
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im a banana!!!!!!!!!!!!!!!

 Nov 1, 2016
 #2
avatar+37099 
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sin a =  tan a     then a =0 degrees     then cos 0  = 1

 Nov 1, 2016
 #3
avatar+129839 
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If sin A = tan A  ....then

 

sin A  = sin A / cos A      multiply both sides by cos A

 

sin A cos A  = sin A     divide both sides by sin A

 

cos A  = sin A / sin A

 

cos A  = 1

 

And   A  = 0°

 

 

 

cool cool cool

 Nov 1, 2016
 #4
avatar+129839 
0

I just realized that I committed a cardinal sin on this one....I cannot divide by sin A....since A  = 0°

 

Here's a correct approach :

 

sin A  = tan A

 

sin A  = sin A / cos A

 

sin A - sin A/ cos A   = 0     factor out sin A

 

sin A [ 1 - 1/cos A]  = 0

 

sin A  [ 1 - sec A ]  = 0

 

So either   sin A  = 0     in which case A = 0°   or   sec A  = 1......which further confirms that A = 0°  .....and cos A  = cos 0°  = 1

 

 

 

cool cool cool

 Nov 2, 2016

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