Solve for E sec(theta)=I/(ER^2)

$\sec (θ) = \frac{I}{E R^{2}}$

Rewrite the equation as $\frac{I}{E R^{2}} = \sec (θ)$ .

$\frac{I}{E R^{2}} = \sec (θ)$

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$E R^{2}, 1$

The LCM of one and any expression is the expression.

$E R^{2}$

Multiply each term in $\frac{I}{E R^{2}} = \sec (θ)$ by $E R^{2}$ to eliminate the fractions.

Multiply each term in $\frac{I}{E R^{2}} = \sec (θ)$ by $E R^{2}$ .

$\frac{I}{E R^{2}} (E R^{2}) = \sec (θ) (E R^{2})$

Simplify the left side.

Cancel the common factor of $E R^{2}$ .

Cancel the common factor.

$\frac{I}{E R^{2}} (E R^{2}) = \sec (θ) (E R^{2})$

Rewrite the expression.

$I = \sec (θ) (E R^{2})$

Simplify the right side.

Reorder factors in $\sec (θ) E R^{2}$ .

$I = E R^{2} \sec (θ)$

Solve the equation.

Rewrite the equation as $E R^{2} \sec (θ) = I$ .

$E R^{2} \sec (θ) = I$

Divide each term in $E R^{2} \sec (θ) = I$ by $R^{2} \sec (θ)$ and simplify.

Divide each term in $E R^{2} \sec (θ) = I$ by $R^{2} \sec (θ)$ .

$\frac{E R^{2} \sec (θ)}{R^{2} \sec (θ)} = \frac{I}{R^{2} \sec (θ)}$

Simplify the left side.

Cancel the common factor of $R^{2}$ .

Cancel the common factor.

$\frac{E R^{2} \sec (θ)}{R^{2} \sec (θ)} = \frac{I}{R^{2} \sec (θ)}$

Rewrite the expression.

$\frac{E \sec (θ)}{\sec (θ)} = \frac{I}{R^{2} \sec (θ)}$

Cancel the common factor of $\sec (θ)$ .

Cancel the common factor.

$\frac{E \sec (θ)}{\sec (θ)} = \frac{I}{R^{2} \sec (θ)}$

Divide $E$ by $1$ .

$E = \frac{I}{R^{2} \sec (θ)}$

Simplify the right side.

Separate fractions.

$E = \frac{I}{R^{2}} \cdot \frac{1}{\sec (θ)}$

Rewrite $\sec (θ)$ in terms of sines and cosines.

$E = \frac{I}{R^{2}} \cdot \frac{1}{\frac{1}{\cos (θ)}}$

Multiply by the reciprocal of the fraction to divide by $\frac{1}{\cos (θ)}$ .

$E = \frac{I}{R^{2}} (1 \cos (θ))$

Multiply $\cos (θ)$ by $1$ .

$E = \frac{I}{R^{2}} \cos (θ)$

Combine $\frac{I}{R^{2}}$ and $\cos (θ)$ .

$E = \frac{I \cos (θ)}{R^{2}}$

Solve for E sec(theta)=I/(ER^2)

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