` (cot 224^(@)-cot 134^(@))/(cot 226^(@)+cot316^(@))` किसके तुल्य है ?

Options

A. ` -"cosec" 88^(@)`
B. ` -"cosec" 2^(@)`
C. ` -"cosec"44^(@)`
D. ` - "cosec" 46^(@)`

Answer

b

Explanation

` (cot 224^(@) - cot 134^(@))/(cot 226^(@)+cot316^(@))`
` (cot (360^(@)-136^(@))-cot(90^(@)+44^(@)))/(cot (360^(@)-134^(@))+cot(360^(@)-44^(@)))`
` [ :' cot (360^(@) - theta) = - cot theta` तथा
` cot (90^(@) +theta)=- tan theta] `
` = (-cot 136^(@) + tan 44^(@))/(-cot 134^(@) - cot 44^(@))`
` = (-cot(90^(@)+46^(@))+tan 44^(@))/(-cot(90^(@)+44^(@))-cot44^(@))`
` = (tan 46^(@) + tan 44^(@))/(tan 44^(@)-cot (90^(@)-46^(@)))`
` [ :' (90^(@) +theta)=- tan theta]`
` (tan46^(@) +tan 44^(@))/(tan 44^(@)- tan 46^(@))`
` [ :' cot (90^(@) - theta)= tan theta] `
` = (((sin 46^(@))/(cos46^(@))+(sin44^(@))/(cos 44^(@))))/(((sin44^(@))/(cos44^(@))- (sin46^(@))/(cos46^(@))))`
` [ :' tan theta = (sin theta)/(cos theta)]`
` (sin 46^(@) cos 44^(@) + sin 44^(@) * cos 46^(@))/(sin 44^(@) * cos 46^(@) - sin 46^(@)* cos 44^(@))`
` = (sin (46^(@)+44^(@)))/(sin(44^(@)-46^(@)))`
` ( sin 90^(@))/(sin (-2)) = 1/(-sin 2^(@))`
` = - cosec 2^(@)`