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Exercise

$x^2\tan y=50$

Step-by-step Solution

1

Multiply the equation by the reciprocal of $x^2$

$\tan\left(y\right)=50x^{-2}$
2

Take the inverse of $\tan\left(y\right)$ on both sides

$\arctan\left(\tan\left(y\right)\right)=\arctan\left(50x^{-2}\right)$
3

Apply the formula: $\arctan\left(\tan\left(\theta \right)\right)$$=\theta $, where $x=y$

$y=\arctan\left(50x^{-2}\right)$
4

Applying the property of exponents, $\displaystyle a^{-n}=\frac{1}{a^n}$, where $n$ is a number

$y=\arctan\left(\frac{50}{x^{2}}\right)$

Final answer to the exercise

$y=\arctan\left(\frac{50}{x^{2}}\right)$

Try other ways to solve this exercise

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