Question

Ето нужно ! 1.) sin2α/ 2sinαcosα - cos2α 2.) sin7α- sin5α / sin7α+ sin5α 3.) cosα+ cos3α+ cos5α / sinα+ sin3α+ sin5α 4.) 2sin40 cos10 cos8 5.) sin2α, cos2α, tg2α если cosα= - 5/13 и sinα> 0

Answer 1

1.) sin2α/ 2sinαcosα - cos2α = 2sinαcosα/2sinαcosα - cos2a = 1 - cos2a = cos^2a + sin^2a - cos^2a + sin^2a = 2sin^2a
2.) sin7α- sin5α / (sin7α+sin5α) = 2cos(12a/2)sin(2a/2)/2sin(12a/2)cos(2a/2) = 2cos(6a)sin(a)/2sin(6a)cos(a) = tg(a)*ctg(6a)
3.) cosα+ cos3α+ cos5α / sinα+ sin3α+ sin5α = cos(3a) + 2cos(6a/2)cos(4a/2)/sin(3a) + 2sin(6a/2)cos(4a/2) = cos(3a)(1+2cos(2a))/sin(3a)(1+2cos(2a)) = ctg(3a)
4.) 2sin40 cos10 cos8  - Между ними стоит знак умножения???
5.) sin2α, cos2α, tg2α если  cosα= - 5/13 и sinα> 0
cos(2a) = 2cos^2(a)-1 = 2*(25/169)-1 = -144/169
sin(a)=$\sqrt{1-cos^{2}(a) } = \sqrt{1- \frac{25}{169} } = \frac{12}{13}$
sin(2a)=2sin(a)cos(a)=2*(-5/13)*(12/13) = -120/169
tg(2a) = sin(2a)/cos(2a) = (-120/169)*(-169/144) = 5/6