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prove that 1/(cosecA-cotA) - 1/sinA = 1/sinA - 1/(cosecA+cotA)

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6 years ago

```							LHS=1/(cosecA-cotA) -1/sinA=(cosecA+cotA)/cosec^2A-cot^2A) -cosecA=cosecA+cotA-cosecA=cotARHS=1/sinA-1/(cosecA+cotA)=cosecA-(cosecA-cotA)/(cosec^2A-cot^2A)=cosecA-(cosecA-cotA)=cotALHS=RHSThanks & RegardsRinkoo GuptaAskIITians Faculty
```
6 years ago
```							1/cosecA-cotA - 1/sinA= 1/sinA - 1/cosecA+cotA Taking LHS 1/(cosecA-cotA )- 1/sinA 1/(cosecA-cotA ) *(cosecA+cotA )/(cosecA +cotA )- 1/sinA (rationalizing the denominator) (cosecA +cotA )/(cosec^2A +cot^2A )-1/sinA As (cosec^2A +cot^2A )=1 (cosecA +cotA ) - 1/sinA 1/sinA +(cotA-cosecA) 1/sinA +(cotA-cosecA)*(cosecA+cotA )/(cosecA+cotA ) (ratioalizing the numerator) 1/sinA +(cot^2A-cosec^2A)/(cosecA+cotA ) 1/sinA +1/(cosecA+cotA ) As (cosec^2A +cot^2A )=1 =RHS
```
3 years ago
```							1/(cosecA-cotA) -1/sinA=(Cosec^2A-cot^2A)/(cosecA-cotA)-cosecA .  (As cosec^2A-cot^2A=1)=(CosecA+cotA)-cosecA=CosecA-(CosecA-cotA)=1/sinA-(cosecA-cotA)(cosecA+cotA)/(cosecA+cotA)=1/sinA-(cosec^2A-cot^2A)/(cosecA+cotA)=1/sinA-1/(cosecA+cotA)=RHS. Proved
```
2 years ago
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