Question

СРОЧНО!!! АЛГЕБРА 10 КЛАСС 100 БАЛЛОВ!

Answer 1

1) sin(105)=sin(60+45)=sin60×sin45+cos60×sin45=V3/2 × V2/2 + 1/2 × V2/2=(V6+V2)/4

2) sin(pi/4+a)-cos(pi/4+a)=

sin(pi/4)cos(a)+cos(pi/4)sin(a)-cos(pi/4)cos(a)+sin(pi/4)sin(a)=

V2/2 cos(a) +V2/2 sin(a) - V2/2 cos(a) +V2/2 sin(a) =V2 × sin(a)

Answer 2

$sin(105 ^{0} ) = sin(60 ^{0} +45 ^{0}) = \ = sin60 ^{0} cos45 ^{0} + cos60 ^{0} sin 45 ^{0} = \ = frac{ sqrt{3} }{2} times frac{ sqrt{2} }{2} + frac{1}{2} times frac{ sqrt{3} }{2} = \ = frac{ sqrt{3}( sqrt{2} + 1)}{4}$
$sin( frac{pi}{4} + alpha ) - cos( frac{pi}{4} + alpha ) = \ = sqrt{2} sin( ( frac{pi}{4} + alpha ) - frac{pi}{4}) = \ = sqrt{2} sin( alpha )$