Question

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

Answer 1

Given that , `sin (A+B)=1`
`sin(A+B)=sin90^(@) rArr A+B =90^(@)` …(1)
and `cos(A-B)=(sqrt(3))/(2)`
`rArr cos(A-B)=cos30^(@) rArr A-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^(@) rArr B=90^(@)-60^(@)=30^(@)`
`:.A=60^(@) and B=30^()@`