Question

Доказать тождество, нижнее

Answer 1

1) cos4a=cos2×2a=cos²2a-sin²2a=

2cos²2a-1.

2) 3-4cos2a+ 2cos²2a-1=

2cos²2a-4cos2a+→

2(cos²2a-2cos2a+1)=

2(cos2a-1)².

3) 3+4cos2a+2cos²2a-1=

2cos²2a+4cos2a+2. →

2(cos²2a+2cos2a+1)=

2(cos2a-1)².

↓

2(cos2a-1)²/2(cos2a+1)=

((cos²a-sin²a-1)/(cos²a-sin²a+1))² =

((1-sin²a-sin²a-1)/(1-sin²a-sin²a+1))²=

((-2sin²a)/(2(1+sin²a))).²=

(-sin²a/cos²a)=

tg⁴a:)))