Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Prove the following identities, where the angles involved are acute angles for which the expressions are defined. cos A- sin A +1/cos A+sin A -1= cosec A + cot A

5. Prove the following identities, where the angles involved are acute angles for which the expressions are defined.

     (v) \frac{\cos A-\sin A+1}{\cos A+\sin A-1}= \csc A+\cot A , using the identity \csc ^{2}A= 1+\cot ^{2}A

            

            

Answers (1)

best_answer

We need to prove -
\frac{\cos A-\sin A+1}{\cos A+\sin A-1}= cosec A+\cot A

Dividing the numerator and denominator by \sin A, we get;

\\=\frac{\cot A-1+\csc A}{\cot A +1-\csc A}\\\\= \frac{(\cot A+\csc A)-(\csc^2 A-\cot^2A)}{\cot A +1-\csc A}\\\\= \frac{(\csc A+\cot A)(1-\csc A+\cot A)}{\cot A +1-\csc A}\\\\= \csc A+\cot A\\\\ =RHS

Hence Proved.

Posted by

manish

View full answer

Similar Questions

Trending Articles/News

anam-khan

CBSE Class 10 board exams 2026 from February 17, May 15; tentative date sheet out for both phases
anam-khan

CBSE launches Integrated Payment System for Class 10, 12 payments; holds principals liable for errors
anam-khan

NEP 2020 gives Indian schools space for new way of learning, with creativity, contemplation

Latest Question