\(\frac{1 + 2sin60°cos60°}{sin60° + cos60°}\) + \(\frac{1 - 2sin60°cos60°}{sin60° - cos60°}\) = ?
Answer & explanation
Correct answer: option 4
\(\frac{1 + 2sin60°cos60°}{sin60° + cos60°}\) + \(\frac{1 - 2sin60°cos60°}{sin60° - cos60°}\)
= \(\frac{1 + 2 × \frac{\sqrt{3}}{2} × \frac{1}{2}}{\frac{\sqrt{3 }}{2} + \frac{1}{2}}\) + \(\frac{1 - 2 × \frac{\sqrt{3}}{2} × \frac{1}{2}}{\frac{\sqrt{3 }}{2} - \frac{1}{2}}\)
=\(\frac{1 + \sqrt{3}}{1 + \sqrt{3}}\) + \(\frac{1 - \sqrt{3}}{\sqrt{3} - 1}\)
= 1 - 1 = 0