If $$I=$$∫$$0$$$$π$$$$2$$ $$cos$$⁡$$($$$$sin$$⁡$$x)dx$$,$$J=$$∫$$0$$$$π$$$$2$$ $$sin$$⁡$$($$$$cos$$⁡$$x)dx$$ and $$K=$$∫$$0$$$$π$$$$2$$ $$cos$$⁡xdx, then

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If $$I=$$∫$$0$$$$π$$$$2$$ $$cos$$⁡$$($$$$sin$$⁡$$x)dx$$,$$J=$$∫$$0$$$$π$$$$2$$ $$sin$$⁡$$($$$$cos$$⁡$$x)dx$$ and $$K=$$∫$$0$$$$π$$$$2$$ $$cos$$⁡xdx, then

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Given that $$I=$$∫$$0$$$$π$$$$2$$ $$cos$$⁡$$($$$$sin$$⁡$$x)dx$$,$$J=$$∫$$0$$$$π$$$$2$$ $$sin$$⁡$$($$$$cos$$⁡$$x)dx$$,$$k=$$∫$$0$$$$π$$$$2$$ $$cos$$⁡xdx We know that $$cos$$⁡$$($$$$sin$$⁡$$x)$$>$$cos$$⁡x>$$sin$$⁡$$($$$$cos$$⁡$$x)$$ for x∈$$0$$,π$$2$$ since sinx cosx     since $$cos$$ function is decreasing $$in0$$,π$$2$$                                                                                                                                                                                                                        ⇒∫$$0$$$$π$$$$2$$ $$cos$$⁡$$($$$$sin$$⁡$$x)dx$$>∫$$0$$$$π$$$$2$$ $$cos$$⁡xdx>∫$$0$$$$π$$$$2$$ $$sin$$⁡$$($$$$cos$$⁡$$x)dx$$⇒I>K>J

If I=∫0π2 cos⁡(sin⁡x)dx,J=∫0π2 sin⁡(cos⁡x)dx and K=∫0π2 cos⁡xdx, then

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