Cos8x-sin8x если tgx=0.5

1) 1+tg²x=1/cos²x ⇒ cos²x = 1 / (1+tg²x) = 1 / (1+0,25) = 4/5

тогда sin²x=1-cos²x=1-4/5=1/5

cos2x=cos²x-sin²x=4/5-1/5=3/5

cos ⁴ x + sin ⁴ x = (cos ² x + sin ² x) - 2 ·cos ² x ·sin ² x = 1 - 2· (4/5) · (1/5) = = 1 - (8/25) = 17/25

cos⁸ x - sin ⁸ x = (cos ⁴ x - sin ⁴ x) (cos ⁴ x + sin ⁴ x) =

= (cos ² x - sin ² x) · (cos ² x - sin ² x) · (cos ⁴ x + sin ⁴ x) =

= cos 2x· (cos ⁴ x + sin ⁴ x) =

= 3/5 · 17/25 = 51/125