Kako poenostavite f (theta) = csc2theta-sec2theta-3tan2theta za trigonometrične funkcije enote theta?

Odgovor:

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

Pojasnilo:

Najprej ponovno napišite kot:#f (theta) = 1 / sin (2theta) -1 / cos (2theta) -sin (2theta) / cos (2theta) #

Potem kot:

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

Uporabili bomo:

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

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

Torej dobimo:

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

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