(cotA+cosecA-1)/(cotA-cosecA+1)=?

Dear Vishnu

[cotA+(cosecA-1)] [cotA-(cosecA-1)]

=cot²A - (cosecA-1)²

=cot²A- cosec²A + 2cosecA -1

=-1+2cosecA -1= 2cosecA -2

All the best.                                                           

AKASH GOYAL

AskiitiansExpert-IIT Delhi

Please feel free to post as many doubts on our discussion forum as you can. We are all IITians and here to help you in your IIT JEE preparation.

Win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.

Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar  respectively : Click here to download the toolbar..

cotA = cosA/sinA , cosecA = 1/sinA

after putting these expression becomes

(cosA + 1 - sinA)/(cosA + sinA + 1)

now , put cosA = 2cos²(A/2) - 1 in numerator &                           [ using cos2a = 2cos²a-1  or  1-2sin²a ]

              cosA = 1 - 2sin²(A/2) in denominator

now expression becomes

 = 2cos(A/2)/2sin(A/2)

 = cot(A/2)

approve my ans if u like it