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:<math>\sin^2 X + \cos^2 X = I</math>
If {{mvar|X}} is a [[diagonal matrix]], {{math|sin ''X''}} and {{math|cos ''X''}} are also diagonal matrices with {{math|(sin ''X'')<sub>''nn''</sub> {{=}} sin(''X<sub>nn</sub>'')}} and {{math|(cos ''X'')<sub>''nn''</sub> {{=}} cos(''X<sub>nn</sub>'')}}, that is, they can be calculated by simply taking the sines or cosines of the
The analogs of the [[trigonometric addition formulas]] are true [[if and only if]] {{mvar|XY {{=}} YX}}:<ref name="Higham" />
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