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If sinA=(2)/(sqrt(5))andcosB=(1)/(sqrt(10)) where A and B are acute angles , then what is A +B equal to ? |
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Answer» `135^(@)` ![]() `thereforecosA=(1)/(sqrt(5))sinB=(3)/(sqrt(10))` `thereforesin(A+B)=sincosB+cosAsinB` `=((2)/(sqrt(15)))((1)/(sqrt(10)))+((1)/(sqrt(5)))((3)/(sqrt(10)))` `=(2)/(sqrt(50))+(3)/(sqrt(50))=(5)/(sqrt(50))=(5)/(sqrt(25xx2))=(5)/(5sqrt(2))=(1)/(sqrt(2))` `sin(A+B)=(1)/(sqrt(2))rArrsin(90+45)=(1)/(sqrt(2))` `(becausesin(90+45)=cos45^(@))` `thereforeA=90^(@)andB=45^(@)` `thereforeA+B=90^(@)+45^(@)=135^(@)` |
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