use the tangent of the sum of two - angles formula to find the exact value of the trigonometric expression…

use the tangent of the sum of two - angles formula to find the exact value of the trigonometric expression without the use of a calculator. tan(7π/12) choose the complete correct formula below by typing the correct value in each of the four parentheses. each of the four parentheses represents the exact value of a trigonometric expression seen in the previous step. select the correct choice below and fill in the answer boxes to complete your choice. (type the terms of your expression in the same order as they appear in the original expression. type exact answers, using radicals as needed. use integers or fractions for any numbers in the expression.) a. tan(7π/12)=(()) + (())/1-(())() b. tan(7π/12)=1-(())()/(())+(()) c. tan(7π/12)=1+(())()/(())-(()) d. tan(7π/12)=(())-(())/1+(())()

use the tangent of the sum of two - angles formula to find the exact value of the trigonometric expression without the use of a calculator. tan(7π/12) choose the complete correct formula below by typing the correct value in each of the four parentheses. each of the four parentheses represents the exact value of a trigonometric expression seen in the previous step. select the correct choice below and fill in the answer boxes to complete your choice. (type the terms of your expression in the same order as they appear in the original expression. type exact answers, using radicals as needed. use integers or fractions for any numbers in the expression.) a. tan(7π/12)=(()) + (())/1-(())() b. tan(7π/12)=1-(())()/(())+(()) c. tan(7π/12)=1+(())()/(())-(()) d. tan(7π/12)=(())-(())/1+(())()

Answer

Explanation:

Step1: Recall tangent - sum formula

The formula for $\tan(A + B)=\frac{\tan A+\tan B}{1 - \tan A\tan B}$. We can write $\frac{7\pi}{12}=\frac{\pi}{3}+\frac{\pi}{4}$.

Step2: Identify A and B

Let $A=\frac{\pi}{3}$ and $B = \frac{\pi}{4}$. Then $\tan(\frac{7\pi}{12})=\tan(\frac{\pi}{3}+\frac{\pi}{4})=\frac{\tan\frac{\pi}{3}+\tan\frac{\pi}{4}}{1-\tan\frac{\pi}{3}\tan\frac{\pi}{4}}$.

Answer:

A. $\tan\left(\frac{7\pi}{12}\right)=\frac{\tan\left(\frac{\pi}{3}\right)+\tan\left(\frac{\pi}{4}\right)}{1 - \tan\left(\frac{\pi}{3}\right)\tan\left(\frac{\pi}{4}\right)}$