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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