if sin A =1/root 5, cos B = 3/root 10 where A and B are positive acute angles , prove that A+B=45.
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Step-by-step explanation:
sinA=1√5,cosA=√1-sin^2A
cosA=2/√5,tanA=sinA/cosA=1/√5/2/√5
tanA=1/2
cosB=3/√10,sinB=1/√10
tanB=1/3
tan(A+B) =tanA+tanB/1-tanA×tanB
tan(A+B) =1/2+1/3÷1-1/2×1/3
tan(A+B) =3+2/6÷1-1/6
tan(A+B) =5/6÷6-1/6
tan(A+B) =5/6÷5/6
tan(A+B)=1
tan(A+B)=tan45°
(A+B)=1
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Step-by-step explanation:
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