Help me??? Please it’s urgent

Mathematics

2 answers:

Elodia [21]3 years ago

8 0

The answer is option 2.

DiKsa [7]3 years ago

4 0

Answer:

$\tt\cfrac{\sqrt{14}}{6}$

Step-by-step explanation:

$\tt\sqrt{\cfrac{7}{18}}= \cfrac{\sqrt{7}}{\sqrt{18}}=\cfrac{\sqrt{7}}{3\sqrt{2}}=\cfrac{\sqrt{7}\cdot\sqrt{2}}{3\sqrt{2}\cdot\sqrt{2}}=\cfrac{\sqrt{7\cdot2}}{3\cdot2} =\cfrac{\sqrt{14}}{6}$

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AveGali [126]

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3 years ago

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aivan3 [116]

Answer:

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2 years ago

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geniusboy [140]

Answer:

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Step-by-step explanation:

$\text{if } cos(\alpha)=\frac{12}{13}\\\text{That must mean we have a triangle with base 12, and hypotenuse 13.}\\\text{Using Pythagoras, we can determine the base of the triangle must be 5.}\\a^2+b^2=c^2 \text{, where c is the hypotenuse and a, b are the two other sides.}\\c^2-b^2=a^2\\\sqrt{c^2-b^2}=a\\\sqrt{13^2-12^2}=\sqrt{169-144}=\sqrt{25}=5\\\text{Therefore, }sin(\alpha) = \frac{5}{12}\\sin(2\alpha)=2sin(\alpha )cos(\alpha)\\\text{(From double angle formulae identities)}\\$

$sin(2\alpha )=2(\frac{5}{12})(\frac{12}{13})=\frac{10}{13}\\cos(2\alpha )=cos^2(\alpha)-sin^2(\alpha)\\cos(2\alpha )=(\frac{12}{13})^2-(\frac{5}{12})^2=\frac{16511}{24336}\\cot(2\alpha)=\frac{cos(2\alpha)}{sin(2\alpha)}=\frac{\frac{16511}{24336}}{\frac{10}{13}}=\frac{16511}{18720}$