Вычислите (2-5cos2a)/(6+10sin2a)-(13+3tg2a)/(10cos2a-15sin2a) если tga=2.

Question

Вычислите (2-5cos2a)/(6+10sin2a)-(13+3tg2a)/(10cos2a-15sin2a) если tga=2.

Answer 1

Cos²a=1:(1+tg²a)=1:(1+4)=1/5
cosa=1/√5
sina=√(1-cos²a)=√(1-1/5)=2/√5
cos2a=cos²a-sin²a=1/5-4/5=-3/5
sin2a=2sinacosa=2*1/√5*2/√5=4/5
tg2a=sin2a/cos2a=-2/3
(2+3)/(6+8)-(13-2)/(-6-12)=5/14+11/18=(45+77)/126=122/126=61/63