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2.41 Appendix: The reciprocal trigonometric functions

The reciprocal trigonometric functions

sec⁡x=1/cos⁡x, cosec⁢x=1/sin⁡x, cot⁡x=1/tan⁡x.\sec x=1/\cos x,\quad{\hbox{cosec}}\,x=1/\sin x,\quad\cot x=1/\tan x.

Here co stands for reciprocal. We use the terms secant, cosecant and cotangent to avoid confusion between these reciprocal functions and the inverse functions which are defined in 1.54 below.

Here, we have obtained new functions by adding, dividing and taking reciprocals of other functions. We now look briefly at other ways of combining functions.