Question

Find the value of tan 18° in fraction

Answer 1

Answer:

$\displaystyle{\tan18=\dfrac{\left(\sqrt{5}-1\right)\sqrt{10+2\sqrt{5}}}{\left(10+2\sqrt{5}}\right)}$

Step-by-step explanation:

We have to find value of tan 18 .

We have value of two ratio

sin 18 = √ 5 - 1 / 4   and cos 18 = 1 / 4 × √ 10 2 √ 5

Now value of tan 18

$\displaystyle{\tan18=\dfrac{\left(\sqrt{5}-1\right)/4}{\left(\sqrt{10+2\sqrt{5}}\right)/4}}\\\\\\\displaystyle{\tan18=\dfrac{\left(\sqrt{5}-1\right)}{\left(\sqrt{10+2\sqrt{5}}\right)}}\\\\\\\displaystyle{\tan18=\dfrac{\left(\sqrt{5}-1\right)}{\left(\sqrt{10+2\sqrt{5}}\right)}\times\frac{\left(\sqrt{10+2\sqrt{5}}\right)}{\left(\sqrt{10+2\sqrt{5}}\right)}}\\\\\\\displaystyle{\tan18=\dfrac{\left(\sqrt{5}-1\right)\sqrt{10+2\sqrt{5}}}{\left(10+2\sqrt{5}}\right)}$

Hence we get answer .

Answer 2

Answer:

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