Question

Вычислите
1)(sin(2arcsin0.75)
2)cos(arcsin(-0,5)
3)arcsin(sin2)
4)tg(2arcsin2/3)
5)sin(arctg2+arctg3)

Answer 1

Ответ:

Объяснение:

1) sin(2arcsin0,75)=2sin(arcsin0,75)cos(arcsin0,75)=

=2*0,75*√1-sin²(arcsin0,75))=1,5*√7/4=3√7/4

2) cos(arcsin(-0,5))=√(1-sin²(arcsin(-0,5)))=√(1-1/4)=√3/2

3) arcsin(sin 2)=2

4)tg(2arcsin2/3)=2tg(arcsin2/3))/(1-tg²(arcsin2/3))=

tg(arcsin2/3)=sin(arcsin2/3)/cos(arcsin2/3)=(2/3)/((√5)/3)=2√5/5

=(2*2√5/5)/(1-4/5)=4√5

5)sin(arctg2+arctg3)=sin(arcsin(2/√5)+arcsin(3/√10))=

=sin(arcsin2/√5)cos(arcsin3/√10)+sin(arcsin3/√10)cos(arcsin2/√5)=

=(2/√5)(1/√10)+(3/√10)(1/√5)=5/(√5√10)=√5/√(2*5)=1/√2=√2/2