Question

True or false (Picture provided)

Answer 1

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:

`sec^(2)x-1=(cosx)/(cscx)\\\\tg^(2)x=(cosx)/((1)/(sinx))\\\\(1-cos2x)/(1+cos2x)=cosxsinx`

Then, evaluating we have:

`(1-cos(2*45))/(1+cos(2*45))=cos(45)*sin(45)\\\\(1-0)/(1+0)=(√(2) )/(2)*(√(2))/(2)\\\\1=((√(2))^(2) )/(4)\\\\1=(2)/(4)\\\\1=(1)/(2)`

Hence, we can see that the equation is not fulfilled, so, 45° is a counterexample for
`sec^(2)x-1=(cosx)/(cscx)` and the answer is true.

Have a nice day!