If (2 sin α /1 + cos â¡ α + sin â¡ α )=(3/4) , then the value of ( 1 - cos α + sin â¡ α /1 + sin â¡ α ) is equal to

Question

If (2 sin α /1 + cos â¡ α + sin â¡ α )=(3/4) , then the value of ( 1 - cos α + sin â¡ α /1 + sin â¡ α ) is equal to (A) 4/3 (B) 3/4 (C) 1/4 (D) 7/4

Tardigrade Admin · Accepted Answer

Let, x=(2 sin α /1 + cos â¡ α + sin â¡ α ) Let, y=(1 - cos α + sin â¡ α /1 + sin â¡ α ). Now, (x/y)=(2 sin α (1 + sin â¡ α )/(1 + sin â¡ α )2 - (cos)2 â¡ α ) ⇒ (x/y)=(2 sin α (1 + sin â¡ α )/1 + (sin)2 â¡ α + 2 sin â¡ α - 1 + (sin)2 â¡ α )=1 ⇒ x=y=3/4

Q. If $\frac{2 s in α}{1 + cos α + s in α} = \frac{3}{4}$ , then the value of $\frac{1 - cos α + s in α}{1 + s in α}$ is equal to

$4/3$

$3/4$

$1/4$

$7/4$

Q. If 1+cos⁡α+sin⁡α2sinα​=43​ , then the value of 1+sin⁡α1−cosα+sin⁡α​ is equal to

4/3

3/4

1/4

7/4

Let, x=1+cos⁡α+sin⁡α2sinα​ Let, y=1+sin⁡α1−cosα+sin⁡α​. Now, yx​=(1+sin⁡α)2−(cos)2⁡α2sinα(1+sin⁡α)​ ⇒yx​=1+(sin)2⁡α+2sin⁡α−1+(sin)2⁡α2sinα(1+sin⁡α)​=1 ⇒x=y=3/4

Q. If $\frac{2 s in α}{1 + cos α + s in α} = \frac{3}{4}$ , then the value of $\frac{1 - cos α + s in α}{1 + s in α}$ is equal to

$4/3$

$3/4$

$1/4$

$7/4$