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

Mar 19, 2018

No $\sin x \cos x > 1$ is not a true statement.

#### Explanation:

As $| \sin x | \le 1$ and $| \cos x | \le 1$ (this is for all angles i.e. for all values of $x$, whatsoever), we cannot have their product $\sin x \cos x > 1$

Further $\sin x \cos x > 1 \implies 2 \sin x \cos x > 2$ i.e. $\sin 2 x > 2$, but we cannot have that.

Graphically, just pick up various values of $x$ and plot $x$ versus $\sin x \cos x$. Graph appears as shown below.

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

Observe that $\sin x \cos x$ cannot have any value greater than $\frac{1}{2}$,

hence $\sin x \cos x > 1$ is not a true statement.