The domain of the $$functionf(x)$$ $$=$$ $$Cos-1($$$$sec$$ $$($$$$cos$$$$-1X))$$ $$+$$ $$sin$$$$-1$$ (Cosec($$$$sin$$$$-1$$ $$X)) is

Question

The domain of the $$functionf(x)$$ $$=$$ $$Cos-1($$$$sec$$ $$($$$$cos$$$$-1X))$$ $$+$$ $$sin$$$$-1$$ (Cosec($$$$sin$$$$-1$$  $$X)) is

Infinity Learn · Accepted Answer

$$f(x)=$$$$cos$$$$-1($$$$sec$$$$($$$$cos$$$$-1x)+$$$$sin$$$$-1(coses($$$$sin$$$$-1x))$$ ⇒         $$-1$$≤$$sec$$$$($$$$cos$$$$-1x)$$≤$$1$$ and      $$-1$$≤cosec $$($$$$sin$$$$-1x)$$≤$$1$$ ⇒                  $$sec$$$$($$$$cos$$$$-1x)=$$±$$1$$ and               cosec $$($$$$sin$$$$-1x)=$$±$$1$$ ⇒$$cos$$$$-1x=0$$,π   and $$sin$$$$-1x=$$π$$2$$,$$-$$π$$2$$ ⇒                        $$x=$$±$$1$$ and $$x=$$±$$1$$ ∴  Domain is $$x=$$±$$1$$

The domain of the function
f(x) = Cos^-1(sec (cos^-1X)) + sin^-1 (Cosec(sin^-1 X)) is

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The domain of the functionf(x) = Cos-1(sec (cos-1X)) + sin-1 (Cosec(sin-1 X)) is

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The domain of the function
f(x) = Cos^-1(sec (cos^-1X)) + sin^-1 (Cosec(sin^-1 X)) is