Verified the following trig identities and show all work csc

Verified the following trig identities and show all work.

csc⁴ t-cot⁴ t = csc²t+cot² t

cosB/1-sinB = secB+tanB

1/csc y-cot y = csc y + cot y

Cot 4u-1/cot 4u+1 = 1-tan 4u/1+tan 4u

(sec t + tan t)² = 1+sin t / 1-sin t

Cos³x –sin³x /cos x-sin x = 1+sin x cos x

Csc x /1+csc x – csc x/ 1-csc x= 2sec² x

(1-tan² theta)² = sec⁴ theta – 4 tan² theta

Solution

1)csc⁴t-cot⁴t

a²-b²=(a-b)(a+b)

=(csc²t-cot²t)(csc²t+cot²t)

=1*(csc²t+cot²t)

=csc²t+cot²t

2)cosB/1-sinB

multiply and divide by (1+sinB)

=cosB(1+sinB)/((1-sinB)(1+sinB))

=cosB(1+sinB)/(1-sin²B)

=cosB(1+sinB)/(cos²B)

=(1+sinB)/cosB

=(1/cosB)+(sinB/cosB)

=secB+tanB