Prove the following identity:

tan² A - sin² A = sin² A tan² A

Prove the following identity:

cot² A - cos² A = cos² A cot² A

Prove the following identity:

tan² A + cot² A + 2 = sec² A cosec² A

Prove the following identity:

sin A (1 + tan A) + cos A (1 + cot A) = sec A + cosec A