Mathematics

Find the value of (frac{tan 60^o – tan 30^o}{tan 60^o + tan 30^o})

Find the value of (frac{tan 60^o – tan 30^o}{tan 60^o + tan 30^o})
  • A.
    (frac{4}{sqrt{3}})
  • B.
    (frac{2}{sqrt{3}})
  • C.
    1
  • D.
    (frac{1}{2})
Correct Answer: Option D
Explanation

(frac{tan 60^o – tan 30^o}{tan 60^o + tan 30^o}= frac{sqrt{3}-frac{1}{sqrt{3}}}{sqrt{3}+frac{1}{sqrt{3}}}\
=left(frac{sqrt{3}sqrt{3}-1}{sqrt{3}}right)div left(frac{sqrt{3}sqrt{3}+1}{sqrt{3}}right)\
=frac{(3-1)}{(3+1)}\
=frac{2}{4}=frac{1}{2})