Тригонометрия- sin(60 + a)-sin(60 - a) = ?

[Гост]

1) sin(60˚ + α)-sin(60˚ - α)

2) 2√2(cos70˚ . sin80˚ + sin70˚ . sin10˚)
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sin(45˚ + α) - sin(45˚ - α)

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[tex]sin(60^\circ + \alpha) - sin (60 ^\circ - \alpha) =[/tex]
[tex]=\cancel {sin60 ^\circ cos \alpha } + cos 60 ^\circ sin \alpha \cancel {- sin60^\circ cos \alpha } + cos60 ^\circ sin \alpha =[/tex]
[tex]=2cos60 ^\circ sin \alpha =[/tex]
[tex]=\cancel {2 }. \frac {1}{\cancel{2}}sin \alpha=[/tex]
[tex]=sin \alpha[/tex]

[tex]\frac {2 \sqrt {2}(cos 70 ^\circ sin 80 ^\circ+sin 70^\circ sin 10 ^\circ}{sin ( 45^\circ + \alpha) - sin (45^\circ - \alpha)}=[/tex]
[tex]=\frac {2 \sqrt {2} { \frac12 [sin (80 ^\circ +70^\circ)+sin (80 ^\circ - 70^\circ)]}{}=[/tex]

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[tex]\frac {2 \sqrt {2}(cos 70 ^\circ sin 80 ^\circ+sin 70^\circ sin 10 ^\circ)}{sin ( 45^\circ + \alpha) - sin (45^\circ - \alpha)}=[/tex]
[tex]=\frac{2 \sqrt {2} ( \frac12 [sin (80 ^\circ +70^\circ)+sin (80 ^\circ - 70^\circ)]+ \frac12 [cos (70^\circ-10^\circ)-cos( 70^\circ+10^\circ)])}{\cancel{sin 45^\circ cos \alpha} + cos45^\circ sin \alpha \cancel {- sin 45^\circ cos \alpha } + cos 45^\circ sin \alpha}=[/tex]
[tex]=\frac{\cancel {2 }\sqrt {2}.\frac{1}{\cancel{2}} (sin 150^\circ+sin 10^\circ+cos 60^\circ-cos 80^\circ]}{2cos45^\circ sin \alpha}=[/tex]
[tex]=\frac{\cancel {\sqrt {2}} (\frac12+sin (90^\circ - 80^\circ)+\frac12-cos 80^\circ]}{ \cancel {2 } \frac {\cancel {\sqrt {2}}}{\cancel{2}} sin \alpha}=[/tex]
[tex]=\frac{1\cancel {+cos 80^\circ}\cancel {-cos 80^\circ}}{sin \alpha}=[/tex]
[tex]=\frac{1}{sin \alpha}[/tex]