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

1 Answer
Shwetank Mauria
Mar 19, 2018

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.

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