For all x in [0,90] show that cos(sinx)>sin(cosx)

I understood the solution given in my book which said

Cosx +sinx

But then

Cosx

Then take sin and cos both sides resp we get two different opposite answers.

Please explain to me where I I have gone wrong.

Ans:
Hello Student,
Please find answer to your question below

I am assuming you meant 90 to be pi/2.
For




sinx will take the value from 0 to 1 in increasing order.


cosx will take the value from 1 to 0.

You can draw the graph of sinx & cosx, it is clearly seen that
,