Question

Cho góc nhọn α:

a,Chứng minh rằng:\(\dfrac{1-tan\alpha}{1+tan\alpha}=\dfrac{cos\alpha-sin\alpha}{cos\alpha+sin\alpha}\)

Answer 1

\(VT=\dfrac{1-\dfrac{sina}{cosa}}{1+\dfrac{sina}{cosa}}=\dfrac{\dfrac{cosa-sina}{cosa}}{\dfrac{cosa+sina}{cosa}}=\dfrac{cosa-sina}{cosa+sina}=VP\)

Answer 2

\(\dfrac{\left(1-tana\right)}{1+tana}=\left(1-\dfrac{sina}{cosa}\right):\left(1+\dfrac{sina}{cosa}\right)\)

\(=\dfrac{cosa-sina}{cosa}:\dfrac{cosa+sina}{cosa}\)

\(=\dfrac{cosa-sina}{cosa+sina}\)

Answer 3

=cosa−sinacosa:cosa+sinacosa=cosa−sinacosa:cosa+sinacosa