Question

1/
1 + tanA=
cotA/1+cotA

​

Answer 1

Answer:

See the step-by-step explanation

Step-by-step explanation:

Proving is as follows:

$\frac{1}{1 \ + \ tanA} = \frac{cotA}{1 \ + \ cotA }\\\\LHS =\\\\\frac{1}{1 \ + \ tanA} = \frac{1}{1 \ + \ \frac{sinA}{cosA}} = \frac{1}{\frac{cosA + sinA}{cosA}}\\= \frac{cosA}{cosA \ + \ sinA}\\\\=\frac{\frac{cosA}{sinA}}{\frac{cosA \ + \ sinA}{sinA}}....Dividing \ numerator \ and \ denominator \ by \ SinA\\\\=\frac{cotA}{\frac{cosA}{sinA} \ + \ \frac{sinA}{sinA}} =\frac{cotA}{cotA \ + \ 1}\\\\= \frac{cotA}{1 \ + \ cotA} = RHS\\\\Hence \ proved$

Therefore from the above solution it is clear that

$\frac{1}{1 \ + \ tanA} = \frac{cotA}{1 \ + \ cotA }$