Math, asked by RIYAprasad, 1 year ago

prove that cosA-sinA/cosA+sinA=cosecA+cotA

Answers

Answered by samaira1112
1
(cosA - sin A + 1)/(cosA + sinA - 1)
Divide numerator and denominator by sinA, we get
=(cosA/sinA - sinA/sinA + 1/sinA)/ (cosA/sinA + sinA/sinA - 1/sinA)
=(cotA - 1 + cosecA)/(cotA+1- cosecA)
= ​(cotA + cosecA- 1)/cotA + 1 - cosecA)​
We know that cosec2A - cot2A= 1
so we replace 1 by cosec2A - cot2A, we get
=[cotA + cosecA - (cosec2A - cot2A)]/(cotA - cosecA + 1)
=[(cotA + cosecA)- (cosecA - cotA)(cosecA+cotA)]/(cotA -cosecA + 1)
taking cosecA + cotA common, we get
=cosecA + cotA[1-(cosecA - cotA)]/(cotA - cosecA + 1)
=cosecA + cotA(1-cosecA + cotA)/(cotA - cosecA +1)
=cosecA + cotA  Proved         


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