Question

plz solve the problem

if you do it, then I would maek you as brainliest ​

Answer 1

LHS = cosA - sin A + 1/cos A + sin A - 1

Dividing both Nr and Dr by sin A

cot A + cosec A - 1/ cot A + 1- cosec A

cotA + cosec A -(cosec^2 A - cot^2A)/cotA + 1 -cosec A

cosec A + cot - {( cosec A + cot A)(cosec A - cot A )}/ cot A + 1- cosec A

cosec A + cot A ( cot A +1- cosec A )/cot A +1 - cosec A

cosec A + cot A = RHS

PLEASE MARK AS BRAINLIST ANSWER..

Answer 2

Answer:

Hope this helps.

$\displaystyle\frac{\cos A-\sin A+1}{\cos A+\sin A-1}\\ \\=\frac{\cot A-1+\csc A}{\cot A+1-\csc A}\\ \\=\frac{(\cot A-1+\csc A)^2}{(\cot A+1-\csc A)(\cot A-1+\csc A)}\\ \\=\frac{\cot^2 A+(\csc A-1)^2+2\cot A(\csc A-1)}{\cot^2 A-(\csc A-1)^2}\\ \\=\frac{(\csc^2 A-1)+(\csc A-1)^2+2\cot A(\csc A-1)}{(\csc^2A-1)-(\csc A-1)^2}\\ \\=\frac{(\csc A-1)\bigl(\csc A+1+\csc A-1+2\cot A\bigr)}{(\csc A-1)\bigl(\csc A+1-\csc A+1\bigr)}\\ \\=\frac{2\csc A+2\cot A}{2}\\ \\=\csc A + \cot A$