My Fourth Problem

Level 2

$tanx =-cotx$

Find $secx$

The answer is 0.

1 solution

Daniel Ellesar
Jan 26, 2015

Substitute tanx = Y

Y = $- \frac{1}{Y}$

$Y^{2}$ = -1

Y = $i$

Now we draw a triangle, where since tanx = i, the opposite is $i$ and the adjacent is 1.

Using Pythagoras we find that the hypotenuse is 0, so secx is $\frac{0}{1} = 0$

There is no solution, of this equation, among the real numbers. Or am I wrong?

Andrea Palma - 6 years ago

In the problem I didn't clarify that x is real. You're quite right that there is no real solution to x, tan (x) or cot (x), but I asked for sec (x), which you can find by the method outlined above or otherwise.

Daniel Ellesar - 6 years ago

In fact x is undefined in this case, but all of the trigonometric functions of x are well defined. sec (x) = csc (x) =0. sin (x) ∞i. cos (x) = ∞. tan (x) = i. cot (x) = -i.

Daniel Ellesar - 6 years ago

@Daniel Ellesar – Thanks for your reply!

Andrea Palma - 6 years ago

My Fourth Problem

The answer is 0.

1 solution

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