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If = 60^(@) and B=30^(@), then show that...

If `= 60^(@) and B=30^(@)`, then show that : sin A cos B+ cos A sin B= sin (A+B)

Text Solution

Verified by Experts

L.H.S.`= sinA cos B+cosA` sin B
`=sin60^(@)cos30^(@)+cos 60^(@) sin 30^(@)`
`=(sqrt(3))/(2)xx(sqrt(3))/(2)+(1)/(2)xx(1)/(2)=(3)/(4)+(1)/(4)=(4)/(4)=1`
R.H.S. `=sin(A+B)= sin (60^(@)+30^(@))=sin90^(@)=1`
`:.` L.H.S = R.H.S.
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