if @ and $ are the acute angles such that sin@=1/2 and cos$=1/3 then @+$ lies in the interval?ans=]pie/3,2pie/3[

sin@=1/2 => cos@=3^1/2

cos$=1/3 =>sin$=(2*2^1/2)/3

Cos(@+$)=cos@cos$-sin@sin$=(1/3^1/2-2^1/2/3)=(1-6^1/2)/3

the value of 6^1/2=0.573 and cos (pie/3)=3^1/2/2=0.868 and cos (2pie/3)=0.5

since value of cos(@+$)lies bettween cos(pie/3) and cos(2pie/3)

thus @+$ lies bettween [pie/3,2pie/3]

Approved