Question

the value of cos θ/1+ sin θ is equal to​

Answer 1

Answer:

➽ ᴇᴄᴏsʏsᴛᴇᴍ ɪs ᴛʜᴀᴛ ɪᴛ ɪs ᴀ ᴄᴏᴍᴍᴜɴɪᴛʏ ᴏʀ ɢʀᴏᴜᴘ ᴏғ ʟɪᴠɪɴɢ ᴏʀɢᴀɴɪsᴍs ᴛʜᴀᴛ ʟɪᴠᴇ ɪɴ ᴀɴᴅ ɪɴᴛᴇʀᴀᴄᴛ ᴡɪᴛʜ ᴇᴀᴄʜ ᴏᴛʜᴇʀ ɪɴ ᴀ sᴘᴇᴄɪғɪᴄ ᴇɴᴠɪʀᴏɴᴍᴇɴᴛ.

Answer 2

:$\huge{\underline{\underbrace{\mathcal\color{gold}{Answer}}}}$

:$\implies\bold{\dfrac{cos\theta}{1+sin\theta}   }$ 

:$\implies\bold{\dfrac{sin(\dfrac{\pi}{2}-\theta)}{1+cos(\dfrac{\pi}{2}-\theta)}  }$ 

:$\implies\bold{\dfrac{2sin(\dfrac{\pi}{4}-\dfrac{\theta}{2}).cos(\dfrac{\pi}{4}-\dfrac{\theta}{2})}{2cos^{2}(\dfrac{\pi}{4}-\dfrac{\theta}{2})}   }$ 

:$\implies\bold{\dfrac{sin(\dfrac{\pi}{4}-\dfrac{\theta}{2})}{cos(\dfrac{\pi}{4}-\dfrac{\theta}{2})}}$ 

:$\dashrightarrow\bold{tan(\dfrac{\pi}{4}-\dfrac{\theta}{2})}$

$\therefore$ Option (C) is the answer of this question