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

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