A trigonometric identity is an equation involving trigonometric ratios of an angle, where the equation holds true for a defined range of values of the angle.
For the right triangle ABC, let 00≤ A ≤900

cos² A + sin² A =1

cos² A =1 - sin² A

sin² A =1 - cos² A`

1 + tan² A = sec² A

 tan² A = sec² A – 1

sec² A - tan² A=1

cot² A + 1 = cosec² A

cot² A = cosec² A – 1

cosec² A - cot² A = 1