COSA - sin A +1
cos A+sin A-1
= cosec A+ cot A, using the identity cosec2 A=1 + cot2 A.
Soluti
noch form of the numerator and denominator of LHS b
Answers
Answer:
To prove that:
cos A - sin A +1
_______________= (cosec A + cot A)²
cos A + sin A -1
LHS
cos A - sin A +1
_______________
cos A + sin A -1
Dividing by sin A in both numerator and denominator,we get:
cot A - 1 + cosec A
→ __________________
cot A + 1 - cosec A
Using the identity,
cosec²A - cot²A=1→(cosec A + cot A)(cosec A - cot A)=1
cot A + cosec A -(cosec A - cot A)(cosec A + cot A)
→_________________________________________________
cot A -cosec A + (cosec A + cot A)(cosec A - cot A)
(cot A + cosec A)[1-(cosec A - cot A)]
→ ___________________________________
- (cosec A cot A)[1-(cosec A -cot A)]
cosec A + cot A
→ _______________
cosec A - cot A
Multiplying and Dividing by cosec A + cot A,
→(cosec A + cot A)²
→RHS
Hence,proved
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