Question

Chứng minh rằng (sin a)/(1 + cos a) + (1 + cos a)/(sin a) = 2/(sin a)

Answer 1

\(VT=\dfrac{sin\alpha}{1+cos\alpha}+\dfrac{1+cos\alpha}{sin\alpha}\)

\(=\dfrac{sin^2\alpha+\left(1+cos\alpha\right)^2}{sin\alpha\left(1+cos\alpha\right)}\)

\(=\dfrac{sin^2\alpha+1+2cos\alpha+cos^2\alpha}{sin\alpha\left(1+cos\alpha\right)}\\ =\dfrac{\left(sin^2\alpha+cos^2\alpha\right)+1+2cos\alpha}{sin\alpha\left(1+cos\alpha\right)}\\ =\dfrac{2+2cos\alpha}{sin\alpha\left(1+cos\alpha\right)}\\ =\dfrac{2\left(1+cos\alpha\right)}{sin\alpha\left(1+cos\alpha\right)}\\ =\dfrac{2}{sin\alpha}=VP\left(dpcm\right)\)