The correct option is A 2√(3) We know tan75=√(3)+1√(3) 1 and 75=√(3) 1√(3)+1 Therefore, tan75 75=√(3)+1√(3) 1 √(3) 1√(3)+1 =3+2√(3)+1 ...

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Integration by Substitution

Find tan 75...

Question

Find $tan 75^{o} - cot 75^{o}$ .

2 \sqrt{3}

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3 \sqrt{2}

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3

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1

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Solution

The correct option is A $2 \sqrt{3}$
We know $tan 75 = \frac{\sqrt{3} + 1}{\sqrt{3} - 1}$
and $cot 75 = \frac{\sqrt{3} - 1}{\sqrt{3} + 1}$
Therefore, $tan 75 - cot 75 = \frac{\sqrt{3} + 1}{\sqrt{3} - 1} - \frac{\sqrt{3} - 1}{\sqrt{3} + 1}$
$= \frac{3 + 2 \sqrt{3} + 1 - 3 + 2 \sqrt{3} - 1}{2}$
$= 2 \sqrt{3}$

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Similar questions

tan 75^{o} + cot 75^{o} = 4

tan 75^{o} = \frac{\sqrt{3} + 1}{2 \sqrt{2}}

t a n 75^{o} = 2 + \sqrt{3}

\frac{1 + \sqrt{3}}{sin A} = \frac{2}{sin B} = \frac{\sqrt{6}}{sin 60^{o}}

∠ A = 75^{o}, ∠ B = 45^{o}

m | | n

p | | q

∠ 1 = 75^{o}

∠ 2 = ∠ 1 + \frac{1}{3}

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