Miten voit tarkistaa identiteetin tanthetacsc ^ 2theta-tantheta = cottheta?

Vastaus:

Alla oleva todistus

Selitys:

#tantheta * csc ^ 2theta - tantheta #

# = sintheta / costheta * (1 / sintheta) ^ 2 - sintheta / costheta #

# = sintheta / costheta * 1 / sin ^ 2theta - sintheta / costheta #

# = 1 / (sinthetacostheta) - sintheta / costheta #

# = (1-sin ^ 2theta) / (sinthetacostheta) #

# = Cos ^ 2theta / (sinthetacostheta) #

# = Costheta / sintheta #

# = Cottheta #

Ota huomioon, että # sin ^ 2theta + cos ^ 2theta = 1 #, siksi # cos ^ 2theta = 1- sin ^ 2theta #

# LHS = tantheta * csc ^ 2theta - tantheta #

# = tantheta (csc ^ 2theta - 1) #

# = tantheta (1 + cot ^ 2theta - 1) #

# = tantheta * cot ^ 2theta #

# = Cottheta = RHS #