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True or False: Trigonometric and inverse-trigonometric functions are differentiable in their respective domain.

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  • A function is said to be continuous on an open interval $(a,b)$ if it is continuous at every point on the interval $(a,b)$.$\mid f\mid$ is defined as $\mid f\mid(x)=\mid f(x)\mid$
Trigonometric and inverse-trigonometric functions are differentiable in their respective domain.
If you refer to the graph of the trigonometric functions,we can easily verify that $\sin x,\cos x,\tan x,\cot x,\sec x,cosec x$ are continuous function in their respective domain.
Similarly the inverse -trigonometric functions $\sin^{-1}x,\cos^{-1}x,\tan^{-1}x,\cot^{-1}x,\sec^{-1}x,cosec ^{-1}x$ are all continuous in their respective domain.
Hence it is a True statement.
answered Jul 5, 2013 by sreemathi.v
 

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