Hello!
The answer is: True.
Why?
A counterexample is a way that we can prove that something is not true about a mathematical equation or expression, it's also considered as an exception to a rule.
So:
[tex]sec^{2}x-1=\frac{cosx}{cscx}\\\\tg^{2}x=\frac{cosx}{\frac{1}{sinx}}\\\\\frac{1-cos2x}{1+cos2x}=cosxsinx[/tex]
Then, evaluating we have:
[tex]\frac{1-cos(2*45)}{1+cos(2*45)}=cos(45)*sin(45)\\\\\frac{1-0}{1+0}=\frac{\sqrt{2} }{2}*\frac{\sqrt{2}}{2}\\\\1=\frac{(\sqrt{2})^{2} }{4}\\\\1=\frac{2}{4}\\\\1=\frac{1}{2}[/tex]
Hence, we can see that the equation is not fulfilled, so, 45° is a counterexample for [tex]sec^{2}x-1=\frac{cosx}{cscx}[/tex] and the answer is true.
Have a nice day!
