Question 442652
We are letting v be defined as {{{sin(theta)}}} and u be defined as {{{cos(theta)}}}.  

We know that {{{sin(theta)^2 + cos(theta)^2 = 1}}}

In this example, we are letting {{{theta = pi/6 = .523598776}}}


Then {{{v = sin(pi/6) = 1/2 = .5}}}
and {{{u = cos(pi/6) = sqrt(3)/2}= .866025}}}

And so u^2 + v^2 = .5^2 + .866025^2 = .25 + .75 = 1

Claiming that {{{sin(theta)^2 + theta^2 = 1}}} as they've done means that {{{theta^2 = cos(theta)^2}}}, which can never happen. Thus their logic is flawed, and that is the error.