Question

rút gọn biểu thức: \(sin^2\alpha.tan\alpha+cos^2\alpha.cot\alpha+2.sin\alpha.cos\alpha\)

Answer 1

\(=sin^2a\cdot\dfrac{sina}{cosa}+cos^2a\cdot\dfrac{cosa}{sina}+sin2a\)

\(=\dfrac{sin^3a}{cosa}+\dfrac{cos^3a}{sina}+sin2a\)

\(=\dfrac{sin^4a+cos^4a}{sina\cdot cosa}+sin2a\)

\(=\dfrac{1+2\cdot sin^2a\cdot cos^2a+2sin^2acos^2a}{sina\cdot cosa}\)

\(=\dfrac{1+4sin^2acos^2a}{sina\cdot cosa}=\dfrac{1+2sin2a}{\dfrac{1}{2}sin2a}\)