Câu hỏi của Jayden Valeria

Question

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

YangSu · Accepted Answer

$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)$Câu trả lời: $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)$

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