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Naya [18.7K]
3 years ago
15

Prove that

TexFormula1" title="2 \tan30 \div 1 + tan ^{2} 30 = sin60" alt="2 \tan30 \div 1 + tan ^{2} 30 = sin60" align="absmiddle" class="latex-formula">
prove that

.

​
Mathematics
1 answer:
iVinArrow [24]3 years ago
3 0

Step-by-step explanation:

2tan 30° / 1 + tan² 30° =

2(⅓√3) /1 + (⅓√3)² =

⅔√3 / 1+ ⅓ =

⅔√3 / 4/3 =

2/4 √3 =

½√3 = sin 60° (proven)

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This can be rewritten in degrees as:

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Now, in our case, \alpha=-230^{\circ}

Therefore, (Equation 1) can be written as:

\theta=n(180^{\circ})+(-1)^n(-230^{\circ})..........(Equation 2)

Now, to find the correct options all that we have to do is replace n by relevant integers and find the values of \theta that match.

For n=2, (Equation 2) gives us: \theta=2\times 180^{\circ}+(-1)^2(-230^{\circ})=360^{\circ}-230^{\circ}=130^{\circ}.

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Only the last option sin(-50^{\circ}) will never match sin(-230^{\circ}) because no integral value of n will ever give \theta=-50^{\circ}

Thus the last option is the correct option.

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