Question

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Answer 1

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Explanation:

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Answer 2

tan(75°) = tan (30 + 45)

Now,

`\tan( A + B) = (\tan A + \tan B)/(1 - \tan A × \tan B) \\`

`\tan( 30 + 45) = (\tan 30 + \tan 45)/(1 - \tan 30 × \tan 45)\\`

Here, we know that

tan 30 = √3 ÷ 3 (Rational)

tan 45 = 1

`tan(75) = \frac{ ( √(3) )/(3) + 1 }{1 - \frac{ \sqrt[]{3} }{3} } \\`

`= ( √(3) + 3)/(3 - √(3) ) * (3 + √(3) )/(3 + √(3) ) \\`

`= (3 √(3) + 3 + 9 + 3 √(3) )/(6) \\`

`= (12 + 6 √(3) )/(6) \\`

Cancel 6 we get,

2 + √3 or 2 + 1.732 = 3.732

Thus, The exact value of tan 75 is 2 + √3

-TheUnknownScientist 72