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angles (a) and (B) are obtuse angles in quadrant 2 (II).If csc a= 3 and tan B= -1/3,determine the exact value for cos (a+b)

 Nov 19, 2020
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From the sum formula for cosine:

 

cos(a + B) = cos a cos B  -  sin a sin B

 

Since  csc a  =  3 :

sin a  =  1/3

 

Since  sin a  =  1/3  and  cos2  a  =  1 - sin2 a   :

cos2a  =  8/9       And since  a  is in quadrant II,

cos a  =  -√8 / 3

 

We can again use the Pythagorean identity and the fact that B is in quadrant II to get:

sin B  =  1/ √10

cos B  =  -3 / √10

 

And so...

 

cos(a + B) = (-√8 / 3)(-3 / √10)  -  (1/3)(1/ √10)

 

Plug this into a calculator or simpify it to get a final answer.....I don't have time to write a better explanation right now, but if you have any questions about this please ask!

 Nov 19, 2020

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