Bagaimanakah anda membuktikan csc ^ 4 [theta] -cot ^ 4 [theta] = 2csc ^ 2-1?

Bagaimanakah anda membuktikan csc ^ 4 [theta] -cot ^ 4 [theta] = 2csc ^ 2-1?
Anonim

Jawapan:

Lihat di bawah

Penjelasan:

Sebelah kiri: # = 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 #

#=#Sebelah kanan