use an identity to simplify the following expression.\n\\frac{\\tan 17^{\\circ}}{1 - \\tan ^{2}…

use an identity to simplify the following expression.\n\\frac{\\tan 17^{\\circ}}{1 - \\tan ^{2} 17^{\\circ}}\n\nchoose the correct expression equal to \\frac{\\tan 17^{\\circ}}{1 - \\tan ^{2} 17^{\\circ}} below.\n\n\\( \\bigcirc \\) a. \\( \\frac{1}{2} \\tan 17^{\\circ} \\)\n\\( \\bigcirc \\) b. \\( \\frac{1}{2} \\cos 17^{\\circ} \\)\n\\( \\bigcirc \\) c. \\( \\frac{1}{2} \\tan 34^{\\circ} \\)\n\\( \\bigcirc \\) d. \\( \\sin 34^{\\circ} \\)

use an identity to simplify the following expression.\n\\frac{\\tan 17^{\\circ}}{1 - \\tan ^{2} 17^{\\circ}}\n\nchoose the correct expression equal to \\frac{\\tan 17^{\\circ}}{1 - \\tan ^{2} 17^{\\circ}} below.\n\n\\( \\bigcirc \\) a. \\( \\frac{1}{2} \\tan 17^{\\circ} \\)\n\\( \\bigcirc \\) b. \\( \\frac{1}{2} \\cos 17^{\\circ} \\)\n\\( \\bigcirc \\) c. \\( \\frac{1}{2} \\tan 34^{\\circ} \\)\n\\( \\bigcirc \\) d. \\( \\sin 34^{\\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 = 17^{\circ}) into the formula

When (\alpha = 17^{\circ}), we have (\frac{\tan17^{\circ}}{1-\tan^{2}17^{\circ}}). Using the formula (\frac{\tan\alpha}{1-\tan^{2}\alpha}=\frac{1}{2}\tan2\alpha), substituting (\alpha = 17^{\circ}) gives (\frac{1}{2}\tan(2\times17^{\circ})). Since (2\times17^{\circ}=34^{\circ}), the expression (\frac{\tan17^{\circ}}{1 - \tan^{2}17^{\circ}}=\frac{1}{2}\tan34^{\circ}).

Answer:

C. (\frac{1}{2}\tan34^{\circ})