Question

prove that 1+tan/1-tan=cot/1-cot=cos+sin

Answer 1

Answer:

$\frac{1+tanA}{1-tanA}\\=\frac{cotA+1}{cotA-1}\\=\frac{cosA+sinA}{cosA-sinA}$

Step-by-step explanation:

$i) \frac{1+tanA}{1-tanA}\\=\frac{1+\frac{1}{cotA}}{1-\frac{1}{cotA}}\\=\frac{cotA+1}{cotA-1}\:--(1)$

$ii)\frac{cotA+1}{cotA-1}\\=\frac{\frac{cosA}{sinA}+1}{\frac{cosA}{sinA}-1}\\=\frac{cosA+sinA}{cosA-sinA}\:--(2)$

Therefore,

$\frac{1+tanA}{1-tanA}\\=\frac{cotA+1}{cotA-1}\\=\frac{cosA+sinA}{cosA-sinA}$

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