Question

Using the graphs to find the value of x, is sin x cos x > 1 a true statement?

Answer 1

No `sinxcosx>1` is not a true statement.

Explanation:

As `|sinx|<=1` and `|cosx|<=1` (this is for all angles i.e. for all values of `x`, whatsoever), we cannot have their product `sinxcosx>1`

Further `sinxcosx>1=>2sinxcosx>2` i.e. `sin2x>2`, but we cannot have that.

Graphically, just pick up various values of `x` and plot `x` versus `sinxcosx`. Graph appears as shown below.

graph{sinxcosx [-5, 5, -1.92, 3.08]}

Observe that `sinxcosx` cannot have any value greater than `1/2`,

hence `sinxcosx>1` is not a true statement.