Find tan(2A), if tan(A)=(84)/(13), and A is in quadrant 1.

Apply double angle formula: Use the double angle formula for tangent, which is tan(2A) = 2tan(A) / (1 - tan^2(A)). Calculation: tan(2A) = 2 * (84/13) / (1 - (84/13)^2).Simplify expression: Simplify the expression for tan(2A). Calculation: tan(2A) = 2 * (84/13) / (1 - (7056/169)).Calculate denominator: Continue simplifying by calculating the denominator. Calculation: 1 - (7056/169) = (169/169) - (7056/169) = -6887/169.Calculate tan(2A): Calculate tan(2A) with the simplified denominator. Calculation: tan(2A) = (168/13) / (-6887/169) = (168/13) * (-169/6887).Simplify multiplication: Simplify the multiplication. Calculation: tan(2A) = -168 * 169 / (13 * 6887).Perform final calculation: Perform the final calculation. Calculation: tan(2A) = -28452 / 89471.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find
tan(2A), if
tan(A)=(84)/(13), and
A is in quadrant 1.

Find $\tan (2 A)$ , if $\tan (A)=\frac{84}{13}$ , and $A$ is in quadrant $1$ .

View step-by-step help

Full solution

Q. Find

\tan (2 A)

, if

\tan (A)=\frac{84}{13}

, and

A

is in quadrant

1

Apply double angle formula: Use the double angle formula for tangent, which is $\tan(2A) = \frac{2\tan(A)}{1 - \tan^2(A)}$ . $\newline$ Calculation: $\tan(2A) = \frac{2 \times (\frac{84}{13})}{1 - (\frac{84}{13})^2}.$
Simplify expression: Simplify the expression for $\tan(2A)$ . $\newline$ Calculation: $\tan(2A) = \frac{2 \times (\frac{84}{13})}{1 - (\frac{7056}{169})}$ .
Calculate denominator: Continue simplifying by calculating the denominator. $\newline$ Calculation: $1 - \left(\frac{7056}{169}\right) = \left(\frac{169}{169}\right) - \left(\frac{7056}{169}\right) = \frac{-6887}{169}$ .
Calculate $\tan(2A)$ : Calculate $\tan(2A)$ with the simplified denominator. $\newline$ Calculation: $\tan(2A) = \frac{168}{13} / \frac{-6887}{169} = \frac{168}{13} \cdot \frac{-169}{6887}$ .
Simplify multiplication: Simplify the multiplication. $\newline$ Calculation: $\tan(2A) = -168 \times 169 / (13 \times 6887)$ .
Perform final calculation: Perform the final calculation. $\newline$ Calculation: $\tan(2A) = -\frac{28452}{89471}$ .