1.

If sin (A+B) =1 and cos (A-B) = (sqrt(3))/(2), then find the values of A and B.

Answer»

Solution :Given that , `SIN (A+B)=1`
`sin(A+B)=sin90^(@) rArr A+B =90^(@)`…(1)
and`cos(A-B)=(SQRT(3))/(2)`
`rArrcos(A-B)=COS30^(@)rArrA-B=30^(@)`...(2)
Adding equations (1)and (2)
`A+B=90^(@)A-B=30^(@)`
`2A=120^(@)rArr A=60^(@)`Put A` 60^(@)` in equation (1)
`60^(@)+B=90^(@)rArrB=90^(@)-60^(@)=30^(@)`
`:.A=60^(@)and B=30^()@`


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