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Mock Nov 22 1H
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Find the exact value of tan 30° x cos 30°
Give your answer in its simplest form.
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LA
Total marks: 2



Answer :

GinnyAnswer
To find the exact value of [tex]\( \tan 30^\circ \times \cos 30^\circ \)[/tex]:

1. Determine [tex]\( \tan 30^\circ \)[/tex]:
[tex]\[ \tan 30^\circ = \frac{1}{\sqrt{3}} \][/tex]
2. Determine [tex]\( \cos 30^\circ \)[/tex]:
[tex]\[ \cos 30^\circ = \frac{\sqrt{3}}{2} \][/tex]

3. Multiply [tex]\( \tan 30^\circ \)[/tex] by [tex]\( \cos 30^\circ \)[/tex]:
[tex]\[ \tan 30^\circ \times \cos 30^\circ = \left(\frac{1}{\sqrt{3}}\right) \times \left(\frac{\sqrt{3}}{2}\right) \][/tex]

4. Simplify the multiplication:
[tex]\[ \left(\frac{1}{\sqrt{3}}\right) \times \left(\frac{\sqrt{3}}{2}\right) = \frac{1 \times \sqrt{3}}{\sqrt{3} \times 2} = \frac{\sqrt{3}}{2\sqrt{3}} = \frac{1}{2} \][/tex]

Therefore, the exact value of [tex]\( \tan 30^\circ \times \cos 30^\circ \)[/tex] in its simplest form is:
[tex]\[ \boxed{\frac{1}{2}} \][/tex]

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