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Let f(x) =x-sinx <br> `f(x) =1 -cosx gt 0,forall in (0,pi//2)` <br> So ,f(x) is an increasing function. <br> for `x in (0,pi//2),f(x)gt0` <br> or x-`sinxgt0` <br> `xgt sin x` <br> Now `cos x in (0,1) for x in (0,pi//2)` <br> So, from (1), we have (replacing x by cosx) <br> cosx `gt` sin (cosx) <br> Also ,cos x is decreasing in `(0,pi//2)` <br> Therefore from (1),we have (applying cos both sides) <br> `cos lt cos (sin x)` <br> from (2) and (3) we get <br> `sin (cos x) lt cos xltcos(sin x)` <br> or `cos (sin x)gt sin (cosx)` Transcript

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00:00 - 00:59 | hello given to prove that X is greater than sign X so for this we apply graphical method for graph of sin x it will be 0 to pi by 2 likes 0 and Pi by 2 for power to the value will be one and 800 for X plot the graph for graph the court will be somewhat like this so from the graphic and see that the value of x is always greater than sign X at each and every point so we can see that X is greater than sign x4x belongings 2022 also we can say that at x = 2 pi by 2 the value the value of Y it will also be 5 by 2 that is 3.142 1.57 at X equal to pi by 2 value will be 1.57 each and every point |

01:00 - 01:59 | this applies to thank you |

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