Question

Please Prove this :
Thank u in advance

Answer 1

Answer:

Step-by-step explanation:

$\dfrac{\sin \dfrac{\theta}{2}-\sqrt{1+\sin \theta}  }{\cos\dfrac{\theta}{2} -\sqrt{1+\sin\theta} }$

(∵$1+\sin \theta=(\sin\dfrac{\theta}{2} +cos\dfrac{\theta}{2})^2$)

then

$\dfrac{\sin \dfrac{\theta}{2}-\sqrt{(\sin\dfrac{\theta}{2} +cos\dfrac{\theta}{2})^2}  }{\cos\dfrac{\theta}{2} -\sqrt{(\sin\dfrac{\theta}{2} +cos\dfrac{\theta}{2})^2} }\\\\=\dfrac{\sin \dfrac{\theta}{2}-{(\sin\dfrac{\theta}{2} +cos\dfrac{\theta}{2})}  }{\cos\dfrac{\theta}{2} -{(\sin\dfrac{\theta}{2} +cos\dfrac{\theta}{2})} }\\\\=\dfrac{\sin \dfrac{\theta}{2}-{\sin\dfrac{\theta}{2} -cos\dfrac{\theta}{2}}  }{\cos\dfrac{\theta}{2} -{\sin\dfrac{\theta}{2} -cos\dfrac{\theta}{2}} }$

$=\dfrac{-\cos \dfrac{\theta}{2} }{-\sin\dfrac{\theta}{2} } \\\\=\cot \dfrac{\theta}{2}$

Answer 2

Answer:

hey mate please refer to the attachment