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Revision:Pythagorean identities

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TSR Wiki > Study Help > Subjects and Revision > Revision Notes > Mathematics > Pythagorean identities

From our definitions of sin and cos, and using Pythagoras' theorem, it is easily seen that


\sin^2x + \cos^2x = 1.


By dividing through by sin²x and cos²x respectively, we end up with the two identities given below. Although sin²x and cos²x can equal 0 (exactly when sin x = 0 and cos x = 0, respectively), our definitions of tan, sec, cosec and cot allow us to divide through.


1 + \cot^2x = \mathrm{cosec}^2 x


\tan^2x + 1 = \sec^2x


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