Kako dokazati csc ^ 4 [teta] -cot ^ 4 [t] = 2csc ^ 2-1?

Odgovor:

Pogledaj ispod

Obrazloženje:

Lijeva strana: # = csc ^ 4 theta - cot ^ 4 theta #

# = 1 / sin ^ 4 theta - cos ^ 4 theta / sin ^ 4 theta #

# = (1-cos ^ 4 theta) / sin ^ 4 theta #

# = ((1 + cos ^ 2 theta) (1-cos ^ 2 theta)) / sin ^ 4 theta #

# = ((1 + cos ^ 2 theta) sin ^ 2 theta) / sin ^ 4 theta #

# = (1 + cos ^ 2 theta) / sin ^ 2 theta #

# = 1 / sin ^ 2 theta + cos ^ 2 theta / sin ^ 2 theta #

# = csc ^ 2 theta + cot ^ 2 theta #---> # cot ^ 2 theta = csc ^ 2 theta -1

# = csc ^ 2 theta + csc ^ 2 theta -1

# = 2csc ^ 2 theta -1 #

#=#Desna strana