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(75°) c. tan(75°)=(tan 30° + tan 45°)/(1 - tan 30° tan 45°) d. tan(75°)=(1 + tan ° tan °)/(tan ° - tan °) choose and complete the 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 from 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 expressions) a. tan(75°)=(1 + )/( - ) b. tan(75°)=( - )/(1 + ) c. tan(75°)=( + )/(1 - ) d. tan(75°)=(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(75°) c. tan(75°)=(tan 30° + tan 45°)/(1 - tan 30° tan 45°) d. tan(75°)=(1 + tan ° tan °)/(tan ° - tan °) choose and complete the 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 from 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 expressions) a. tan(75°)=(1 + )/( - ) b. tan(75°)=( - )/(1 + ) c. tan(75°)=( + )/(1 - ) d. tan(75°)=(1 - )/( + )

Answer

Explanation:

Step1: Express 75° as a sum of angles

We know that (75^{\circ}=30^{\circ} + 45^{\circ}). The formula for (\tan(A + B)=\frac{\tan A+\tan B}{1 - \tan A\tan B}). Here (A = 30^{\circ}) and (B=45^{\circ}).

Step2: Recall the tangent - values of special angles

(\tan30^{\circ}=\frac{\sqrt{3}}{3}) and (\tan45^{\circ}=1).

Step3: Substitute the values into the formula

(\tan(75^{\circ})=\tan(30^{\circ}+45^{\circ})=\frac{\tan30^{\circ}+\tan45^{\circ}}{1 - \tan30^{\circ}\tan45^{\circ}}=\frac{\frac{\sqrt{3}}{3}+ 1}{1-\frac{\sqrt{3}}{3}\times1}).

Answer:

(\tan(75^{\circ})=\frac{\frac{\sqrt{3}}{3}+ 1}{1-\frac{\sqrt{3}}{3}\times1}), and the correct choice from the given options is C. (\tan(75^{\circ})=\frac{\tan30^{\circ}+\tan45^{\circ}}{1 - \tan30^{\circ}\tan45^{\circ}}) (where the filled - in values in the general form of option C are (\tan30^{\circ}), (\tan45^{\circ}), (\tan30^{\circ}), (\tan45^{\circ}))