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.