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:

$sec^{2}x-1=\frac{cosx}{cscx}\\\\tg^{2}x=\frac{cosx}{\frac{1}{sinx}}\\\\\frac{1-cos2x}{1+cos2x}=cosxsinx$

Then, evaluating we have:

$\frac{1-cos(2*45)}{1+cos(2*45)}=cos(45)*sin(45)\\\\\frac{1-0}{1+0}=\frac{\sqrt{2} }{2}*\frac{\sqrt{2}}{2}\\\\1=\frac{(\sqrt{2})^{2} }{4}\\\\1=\frac{2}{4}\\\\1=\frac{1}{2}$

Hence, we can see that the equation is not fulfilled, so, 45° is a counterexample for $sec^{2}x-1=\frac{cosx}{cscx}$ and the answer is true.

Have a nice day!

3 0

4 years ago

Elena makes her favorite shade of purple paint by mixing 3 cups of blue paint, 1 1/2 cups of red paint, and 1/2 of a cup of whit

elena-s [515]

Answer: 1/3 cup

Step-by-step explanation:

8 0

3 years ago

1. Determine whether the regular hexagon has reflection symmetry, rotation symmetry, both, or neither. If it has reflection symm

lana [24]

The regular hexagon has both reflection symmetry and rotation symmetry.

Reflection symmetry is present when a figure has one or more lines of symmetry. A regular hexagon has 6 lines of symmetry. It has a 6-fold rotation axis.

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Rotation symmetry is present when a figure can be rotated (less than 360°) and still look the same as before it was rotated. The center of rotation is a point a figure is rotated around such that the rotation symmetry holds. A regular hexagon can be rotated 6 times at an angle of 60°

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3 0

4 years ago

Compare lengths. Write >, <, or = .<br><br> 22 ft __ 7 yd 11 in.

Tomtit [17]

22ft is less than 7yd 11in

6 0

3 years ago