Math Doubts

Cofunction identities

A trigonometric identity of two trigonometric functions which contain complementary angles is called cofunction identity.

There are six cofunction identities in trigonometry. Each cofunction identity is written in two different styles. In trigonometry, theta ($\theta$) symbol is used to represent angle in degrees and $x$ is used to represent angle in radians.

Cofunction identity of Sin function

$\sin{(90^\circ-\theta)} \,=\, \cos{\theta}$

$\sin{\Big(\dfrac{\pi}{2}-x\Big)} \,=\, \cos{x}$

Cofunction identity of Cos function

$\cos{(90^\circ-\theta)} \,=\, \sin{\theta}$

$\cos{\Big(\dfrac{\pi}{2}-x\Big)} \,=\, \sin{x}$

Cofunction identity of Tan function

$\tan{(90^\circ-\theta)} \,=\, \cot{\theta}$

$\tan{\Big(\dfrac{\pi}{2}-x\Big)} \,=\, \cot{x}$

Cofunction identity of Cot function

$\cot{(90^\circ-\theta)} \,=\, \tan{\theta}$

$\cot{\Big(\dfrac{\pi}{2}-x\Big)} \,=\, \tan{x}$

Cofunction identity of Sec function

$\sec{(90^\circ-\theta)} \,=\, \csc{\theta}$

$\sec{\Big(\dfrac{\pi}{2}-x\Big)} \,=\, \csc{x}$

Cofunction identity of Cosec function

$\csc{(90^\circ-\theta)} \,=\, \sec{\theta}$

$\csc{\Big(\dfrac{\pi}{2}-x\Big)} \,=\, \sec{x}$



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