Please give me the proof for " absolute value of cos x is less than or equal to absolute value of x? "
Here is a small problem which is related to the given question. prove y=f(x)=x-sinx >=0 for all x>=0
take dy/dx=1-cosx >=0 for all x, y is increasing func, f(x) >= f(0) = 0 for all x>=0
then we can easily extend this solution to solve |sinx| <= |x|
but isn't this amazing see graph in this link graph of sin - Google Search
in this graph sinx does never equal 0,
except only at zero
I was expecting it to be zero at pi, 2pi, 3pi ..... and so on, everywhere on (i-e n(pi)) where n belongs to Z+