Sin t+ cos t =0,5
Возведем обе части в квадрат:
sin²t+2sint·cost+cos²t=0,25
1+2sint·cost=0,25
sint·cost=(0,25-1)/2
sin²t\cdot cos²t=(-0,75)²/4=0,140625
sin²t+cos²t=1
Возводим в квадрат
sin⁴t+2sin²t·cos²t+cos⁴t=1
sin⁴t+cos⁴t=1-2sin²tcos²t
sin⁴t+cos⁴t=1-2·0,140625
sin⁴t+cos⁴t=0,71875
![tg^2t+ctg^2t= \frac{sin^2t}{cos^2t} + \frac{cos^2t}{sin^2t}= \frac{sin^4t+cos^4t}{sin^2t\cdot cos^2t}=](https://tex.z-dn.net/?f=tg%5E2t%2Bctg%5E2t%3D+%5Cfrac%7Bsin%5E2t%7D%7Bcos%5E2t%7D+%2B+%5Cfrac%7Bcos%5E2t%7D%7Bsin%5E2t%7D%3D+%5Cfrac%7Bsin%5E4t%2Bcos%5E4t%7D%7Bsin%5E2t%5Ccdot+cos%5E2t%7D%3D)
=0,71875:0,140625=5,11111