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  1. Draw a 30-60-90 triangle. Label all angle measures and side relationships. Using the side relationships from the figure, show that the following trigonometric identities hold true for the given angles:


Atan(60)=sin(60)/cos(60)

Bsin^2(30)+cos^2(30)

Verified Answer :

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Answer with explanation:

Drawing a triangle having angle measurement ,30°,60°,90°.

A.

\(tan 60^{\circ}=\frac{k\sqrt{3}}{1k}=\sqrt{3}\\\\ \frac{sin 60^{\circ}}{cos 60^{\circ}}=\frac{\frac{k\sqrt{3}}{2k}}{\frac{k}{2k}}=\sqrt{3}\\\\\text{as},tan A=\frac{sin A}{cos A}\)

B.

\(sin^2 30^{\circ} + cos^2 30^{\circ}=[\frac{k}{2k}]^2+[\frac{k\sqrt{3}}{2k}]^2\\\\=\frac{1}{4}+\frac{3}{4}\\\\=\frac{4}{4}=1\\\\ \text{as}, Sin ^2 A +Cos ^2 A=1\)

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