Question

The maximum value of sinx . cosx is..

Answer 1

the maximum value of sinx is 1 at x=90 degree sinx =1
the maximum value of cosx is 1 at x=0 degree and x=360degree
∴the product of sinx and cosx = 1x1 =1

Answer 2

Sinx have its highest value when X = 90°
i.e, Sin 90 = 1 
     from Sin 90 onwards the value of sin decreases.
example: Sin 95 =0.995

∴ maximum value for sin is 1

Now considering Cosx, 
maximum value is at 0°
I.e Cos 0 = 1
let us consider an angle greater than 0, then value decreases from 1
For example, Cos 5 = 0.996 

∴ Maximum value for cos is 1

Sinx · Cosx = 1 × 1
                   = 1 //