Prove each of these identities.

a. a/tan x + cot x = sin x cos x

b. sin² x + cos² x/cos² x = sec² x

c. sin² x cos x + cos³ x/sin x = cot x

d. sin² x + cos² x/cos² x = sec² x

e. 1 + tan² x/ tan x = sec x cosec x

f. sin x/1 – cos² x = cosec x

g. sin x tan² x/1 + tan² x = sin³ x

h. 1 – sec² x/1 – cosec² x = tan⁴ x

i. 1 + sin x/1 – sin x = (tan x + sec x)²

j. cos x cot x/cos x + cot x = sec x – tan x