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Elena-2011 [213]
1 year ago
7

Find the exact value by using a half angle identity.tan 75°

Mathematics
1 answer:
kramer1 year ago
5 0

The trigonometric function is given as

\tan 75^{\circ}

Apply the half angle identity to find the value of tan 75 ,

\tan (\frac{u}{2})=\frac{\sin u}{1+\cos u}

Here,

\tan (\frac{150^{\circ}}{2})=\frac{\sin150^{\circ}}{1+cos150^{\circ}}\tan (75^{\circ})=\frac{\frac{1}{2}}{1-\frac{\sqrt[]{3}}{2}}=\frac{\frac{1}{2}}{\frac{2-\sqrt[]{3}}{2}}^{}\tan 75^{\circ}=\frac{1}{2-\sqrt[]{3}}

Now rationalize the function.

\tan 75^{\circ}=\frac{1}{2-\sqrt[]{3}}\times\frac{2+\sqrt[]{3}}{2+\sqrt[]{3}}=\frac{2+\sqrt[]{3}}{4-3}=\frac{2+\sqrt[]{3}}{1}

Again simplify the trigonometric function,

\tan 75^{\circ}=2+1.732=3.732

Hence the answer is 3.732.

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