use identities to write the following expression as a function of z alone. tan (60° + z) choose the correct…

use identities to write the following expression as a function of z alone. tan (60° + z) choose the correct answer below. a. \frac{sqrt{3}-\tan z}{1+sqrt{3} \tan z} b. \frac{sqrt{3}+\tan z}{1-sqrt{3} \tan z} c. \frac{sqrt{3}-2 \tan z}{sqrt{3}+2 \tan z} d. \frac{sqrt{3}+2 \tan z}{sqrt{3}-2 \tan z}

use identities to write the following expression as a function of z alone. tan (60° + z) choose the correct answer below. a. \frac{sqrt{3}-\tan z}{1+sqrt{3} \tan z} b. \frac{sqrt{3}+\tan z}{1-sqrt{3} \tan z} c. \frac{sqrt{3}-2 \tan z}{sqrt{3}+2 \tan z} d. \frac{sqrt{3}+2 \tan z}{sqrt{3}-2 \tan z}

Answer

Explanation:

Step1: Apply the tangent addition formula

The tangent addition formula is (\tan(A + B)=\frac{\tan A+\tan B}{1-\tan A\tan B}). Here (A = 60^{\circ}) and (B=z). We know that (\tan60^{\circ}=\sqrt{3}). Substituting (A = 60^{\circ}) and (B = z) into the formula, we get (\tan(60^{\circ}+z)=\frac{\tan60^{\circ}+\tan z}{1 - \tan60^{\circ}\tan z}).

Step2: Substitute the value of (\tan60^{\circ})

Since (\tan60^{\circ}=\sqrt{3}), the expression becomes (\frac{\sqrt{3}+\tan z}{1-\sqrt{3}\tan z}).

Answer:

B. (\frac{\sqrt{3}+\tan z}{1 - \sqrt{3}\tan z})