use an identity to simplify the following expression.\n\\frac{\\tan 13^{\\circ}}{1 - \\tan ^{2}…

use an identity to simplify the following expression.\n\\frac{\\tan 13^{\\circ}}{1 - \\tan ^{2} 13^{\\circ}}\nchoose the correct expression equal to \\frac{\\tan 13^{\\circ}}{1 - \\tan ^{2} 13^{\\circ}} below.\n\\bigcirc a. \\frac{1}{2} \\tan 13^{\\circ}\n\\bigcirc b. \\frac{1}{2} \\tan 26^{\\circ}\n\\bigcirc c. \\sin 26^{\\circ}\n\\bigcirc d. \\frac{1}{2} \\cos 13^{\\circ}

use an identity to simplify the following expression.\n\\frac{\\tan 13^{\\circ}}{1 - \\tan ^{2} 13^{\\circ}}\nchoose the correct expression equal to \\frac{\\tan 13^{\\circ}}{1 - \\tan ^{2} 13^{\\circ}} below.\n\\bigcirc a. \\frac{1}{2} \\tan 13^{\\circ}\n\\bigcirc b. \\frac{1}{2} \\tan 26^{\\circ}\n\\bigcirc c. \\sin 26^{\\circ}\n\\bigcirc d. \\frac{1}{2} \\cos 13^{\\circ}

Answer

Explanation:

Step1: Recall the double - angle formula for tangent

The double - angle formula for tangent is (\tan2\alpha=\frac{2\tan\alpha}{1 - \tan^{2}\alpha}). We can rewrite it as (\frac{\tan\alpha}{1-\tan^{2}\alpha}=\frac{1}{2}\tan2\alpha).

Step2: Substitute (\alpha = 13^{\circ}) into the formula

When (\alpha = 13^{\circ}), we have (\frac{\tan13^{\circ}}{1-\tan^{2}13^{\circ}}). Using the formula (\frac{\tan\alpha}{1-\tan^{2}\alpha}=\frac{1}{2}\tan2\alpha), substituting (\alpha = 13^{\circ}) gives (\frac{1}{2}\tan(2\times13^{\circ})). Since (2\times13^{\circ}=26^{\circ}), the expression becomes (\frac{1}{2}\tan26^{\circ}).

Answer:

B. (\frac{1}{2}\tan26^{\circ})