1.

If sinA=(2)/(sqrt(5))andcosB=(1)/(sqrt(10)) where A and B are acute angles , then what is A +B equal to ?

Answer»

`135^(@)`
`90^(@)`
`75^(@)`
`60^(@)`

SOLUTION :Given , `sinA=(2)/(sqrt(5))andcosB=(2)/(sqrt(10))`

`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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