Question

When doing trig, I came across this puzzler: http://mathb.in/433 Why is this so? W|A confirms: http://bit.ly/JmEk6p

Answer 1

Secant is the reciprocal function of cosine.

So, if you take the secant of both sides, you get x = sec(cos^-1(1/x))
Since sec = 1/cos;
x = 1/cos(cos^-1(1/x))
= 1/(1/x)
= x

Answer 2

That's kind of a non-rigorous way of showing it, I guess. :P

Answer 3

\[y=cosx\]
\[x=\cos^{-1}y \]
\[1/y = 1/cosx = secx\]
\[\sec^{-1} 1/y = x\]
so there comes your ans wer

Answer 4

In the triangle
\[\sec y=\frac{x}{1}\]
\[\cos y=\frac{1}{x}\]