If x and y are acute angles such that cos x + cos y = 3/2 and sinx + siny = 3/4 then the value of sin ( x + y)

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Solution

Sinx+siny=2 (sin x+y/2)×( cos x-y/2) = 3/4
&
Cosx+cosy=2 (cos x+y/2)× (cos x-y/2) = 3/2

Now divide
tan (x+y/2) = 1/2

Now

Sin(x+y)
= (2 tan(x+y/2))/(1 + tan² (x+y/2))

= (2/2) /(1 + 1/4)

= 1/(5/4)
=4/5

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