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Exercise

$w=\frac{\tan\left(u\right)}{\tan\left(u\right)x\cos\left(u\right)+\sin\left(v\right)}$

Step-by-step Solution

1

Applying the tangent identity: $\displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}$

$w=\frac{\tan\left(u\right)}{x\frac{\sin\left(u\right)}{\cos\left(u\right)}\cos\left(u\right)+\sin\left(v\right)}$
Why is tan(x) = sin(x)/cos(x) ?
2

Multiplying the fraction by $x\cos\left(u\right)$

$w=\frac{\tan\left(u\right)}{x\sin\left(u\right)+\sin\left(v\right)}$

Final answer to the exercise

$w=\frac{\tan\left(u\right)}{x\sin\left(u\right)+\sin\left(v\right)}$

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$\frac{2x+3}{3x}=\frac{x}{2x-3}$

$\frac{x+1}{x-2}=\frac{x-3}{x}$

$\frac{x}{2}=\frac{8}{x}$

Main Topic: Equations

In mathematics, an equation is a statement of an equality containing one or more variables. Solving the equation consists of determining which values of the variables make the equality true. In this situation, variables are also known as unknowns and the values which satisfy the equality are known as solutions.

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