If [$$sin$$–$$1$$ $$cos$$–$$1$$ $$sin$$–$$1$$ $$tan$$–$$1$$ θ ] $$=$$ $$1$$, where [.] denotes the greatest integer function, the θ lies in the interval

Question

Infinity Learn · Accepted Answer

We have, $$sin$$−$$1$$⁡$$cos$$−$$1$$⁡$$sin$$−$$1$$⁡$$tan$$−$$1$$⁡θ$$=1$$⇒$$1$$≤$$sin$$−$$1$$⁡$$cos$$−$$1$$⁡$$sin$$−$$1$$⁡$$tan$$−$$1$$⁡θ≤π$$2$$⇒$$sin$$⁡$$1$$≤$$cos$$−$$1$$⁡$$sin$$−$$1$$⁡$$tan$$−$$1$$⁡θ≤$$1$$⇒$$cos$$⁡$$sin$$⁡$$1$$≥$$sin$$−$$1$$⁡$$tan$$−$$1$$⁡θ≥$$cos$$⁡$$1$$⇒$$sin$$⁡$$cos$$⁡$$sin$$⁡$$1$$≥$$tan$$−$$1$$⁡θ≥$$sin$$⁡$$cos$$⁡$$1$$⇒$$tan$$⁡$$sin$$⁡$$cos$$⁡$$sin$$⁡$$1$$≥θ≥$$tan$$⁡$$sin$$⁡$$cos$$⁡$$1$$

If [sin^–1 cos^–1 sin^–1 tan^–1 θ ] = 1, where [.] denotes the greatest integer function, the θ lies in the interval

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

If [sin–1 cos–1 sin–1 tan–1 θ ] = 1, where [.] denotes the greatest integer function, the θ lies in the interval

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

If [sin^–1 cos^–1 sin^–1 tan^–1 θ ] = 1, where [.] denotes the greatest integer function, the θ lies in the interval