Найти:

1. sin2a+cos2a, если sina=-0,6, п

1) сosa=-√1-0,36=-0,8

2sinacosa+cos²a-sin²a=2 * (-0,8) * (-0,6) + (-0,6) ² - (-0,8) ²=0,96+0,36-0,64=0,68

2) cosa=√1-0,64=0,6

cos²a-sin²a+6sina/cosa=0,36-0,64+6 * (-0,8) / 0,6=-0,28-8=-8,28

3) sin (π/4-a) = sinπ/4cosa-cosπ/4sina=√2/2 (cosa-sina) = √3/8⇒ cosa-sina=√3/8:1/√2=√3/8*√2=√6/8

(cosa-sina) ²=cos²a+sin²a-2cosasina=1-sin2a = (√6/8) ²=6/64=3/32⇒

sin2a=1-3/32=29/32

4) cos (a+π/4) = cosacosπ/4-sinasinπ/4=√2/2 (cosa-sina) = √5/8⇒ cosa-sina=√5/8:1/√2=√5/8*√2=√10/8

(cosa-sina) ²=cos²a+sin²a-2cosasina=1-sin2a = (√10/8) ²=10/64=5/32

sin2a=1-5/32=27/32