вычислите значения выражения а) cos75+cos15-sin75-sin15 б) sin30 cos15+cos30 sin15. Created by anutka9642. algebra-ru

вычислите значения выражения а) cos75+cos15-sin75-sin15 б) sin30 cos15+cos30 sin...

СовушкинДомик

Ответ:

Объяснение:

а) cos75+cos15-(sin75+sin15)

=2cos(90/2)cos(60/2)- 2sin(90/2) cos(60/2)==2cos45cos30-2sin45cos30=0

$2\frac{\sqrt{2} }{2} \frac{\sqrt{3} }{2}- 2\frac{\sqrt{2} }{2} \frac{\sqrt{3} }{2}=0$

б) sin30 cos15+cos30 sin15=sin(30+15)=sin45°=√2/2

afet74

Verified answer

А)cos75=cos(45+30)
cos15=cos(45-30)
sin75=sin(45+30)
sin15=sin(45-30)

Расписываем сумму и разность синусов и косинусов,используя формулы:
cos45cos30-sin45sin30 + cos45cos30+sin45sin30 - sin45cos30- cos45sin30 - sin45cos30+cos45sin30 = 2cos45cos30 -2sin45cos30 = 2* √2/2* √3/2 - 2* √2/2* √3/2= 0

б)sin30° cos15°+cos30° sin15°= sin(30°+15°)= sin45°=√2/2

Answers & Comments

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