If y = (2 sin α/1 + cos α + sin α) then ( 1 - cos α + sin α /1 + sin α) is equal to

Question

If y = (2 sin α/1 + cos α + sin α) then ( 1 - cos α + sin α /1 + sin α) is equal to (A) 1 + y (B) 1 - y (C) (1/y) (D) y

Tardigrade Admin · Accepted Answer

Now, (1- cos α + sin α/1 + sin α) = ((1- cosα + sinα) (1+ cosα + sinα)/(1+ sinα)(1+ cos α + sinα)) = ((1+ sin α)2 - cos2α/(1+ sin α)(1+ cosα + sinα) ) = (1+ sin2 α+ 2 sin α-(1 - sin2 α)/(1+ sinα)(1+ cosα + sinα)) =(1+ sin 2 α+2 sin α-1+ sin 2 α/(1+ sin α)(1+ cos α+ sin α)) =(2 sin α+2 sin 2 α/(1+ sin α)(1+ cos α+ sin α)) =(2 sin α(1+ sin α)/(1+ sin α)(1+ cos α+ sin α)) =(2 sin α/1+ cos α+ sin α) =y

Q. If $y = \frac{2 s i n α}{1 + c o s α + s i n α}$ then $\frac{1 - c o s α + s i n α}{1 + s i n α}$ is equal to

1 + y

1 - y

$\frac{1}{y}$

y

Q. If y=1+cosα+sinα2sinα​ then 1+sinα1−cosα+sinα​ is equal to

1 + y

1 - y

y1​

y

Q. If $y = \frac{2 s i n α}{1 + c o s α + s i n α}$ then $\frac{1 - c o s α + s i n α}{1 + s i n α}$ is equal to

$\frac{1}{y}$