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Trigonometric Exponentiation Equation (Posted on 2024-08-25)

Solve the equation

(sin x)^{tan x}=(cos x)^{cot x}

No Solution Yet Submitted by Danish Ahmed Khan

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Obvious(?) answer

Comment 1 of 1

A quick graph shows the solution to be pi/4.

This is pretty obvious because sin(pi/4)=cos(pi/4) and tan(pi/4)=cot(pi/4).

A unit circle approach doesn't seem to help

y^(y/x) = x^(x/y) where x^2+y^2=1

If you sub y=sqrt(1-x^2) then Wolfram|Alpha won't even give the exact solutionx=sqrt(1/2).

Posted by Jer on 2024-08-25 12:00:59

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