Task/25526933
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Вычислить
sin(3195°)cos(19π/6) +sin²(2017°)+(1/2)*cos(4034°)+cos(π/3)
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sin(3195°)cos(19π/6) +sin²(2017°)+(1/2)*cos(4034°)+cos(π/3) =
sin(9*360°-45°)cos(3π+π/6)+(1/2)*(1-cos(2*2017°) +(1/2)*cos(4034°)+
cos(π/3) = -sin(45°)*(-cos(π/6)+1/2 -(1/2)*cos(4034°)+ 1/2)*cos(4034°)+
+1/2= sin(45°)*cos(π/6)+1 =(√2) /2)* (√3) /2 +1 =(4+√6 ) / 4 .
* * * sin(45°) =(√2) /2 ; cos(π/6)=(√3)/2) ; sin²α =(1-cos2α) /2 и формулы приведения .
проверьте арифметику