Kako pojednostaviti f (theta) = csc2theta-sec2theta-3tan2theta na trigonometrijske funkcije jedinice theta?

Odgovor:

#F (theta) = (cos ^ 2 theta-sin ^ 2 theta-2costhetasintheta-4sin ^ 2thetacos ^ 2 theta) / (2sinthetacos ^ 3theta-sin ^ 3thetacostheta) #

Obrazloženje:

Prvo, prepišite kao:#F (theta) = 1 / sin (2 theta) -1 / cos (2 theta) -sin (2 theta) / cos (2 theta) #

Zatim kao:

#F (theta) = 1 / sin (2 theta) - (1-sin (2 theta)) / cos (2 theta) = (cos (2 theta) -sin (2 theta) -sin ^ 2 (2 theta)) / (sin (2 theta) cos (2 theta)) *

Koristit ćemo:

#cos (A + B) = cosAcosB-sinAsinB #

#sin (A + B) + = sinAcosB cosAsinB #

Dakle, dobivamo:

#F (theta) = (cos ^ 2 theta-sin ^ 2 theta-2costhetasintheta-4sin ^ 2thetacos ^ 2 theta) / ((2sinthetacostheta) (cos ^ 2 theta-sin ^ 2 theta)) *

#F (theta) = (cos ^ 2 theta-sin ^ 2 theta-2costhetasintheta-4sin ^ 2thetacos ^ 2 theta) / (2sinthetacos ^ 3theta-sin ^ 3thetacostheta) #