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Prove that: (secA-cosecA)(1+tanA+cotA)=tanAsecA-cotAcosecA

Prove that:
(secA-cosecA)(1+tanA+cotA)=tanAsecA-cotAcosecA

Grade:11

1 Answers

Rhyth Mehta
34 Points
4 years ago
> Simplifying LHS we get,
 
secA + secA\cdot tanA + secA\cdot cotA - cosecA - cosecA\cdot tanA - cosecA\cdot cotA
 
> Convert all terms into sin & cos  
 
\frac{1}{cosA} + \frac{1}{cosA}\cdot \frac{sinA}{cosA} + \frac{1}{cosA}\cdot \frac{cosA}{sinA} - \frac{1}{sinA} - \frac{1}{sinA}\cdot \frac{sinA}{cosA}- \frac{1}{sinA}\cdot \frac{cosA}{sinA}
 
> After doing little maths, very basic multiplication and division, and converting back from sin and cos to tan, sec, cot and cosec, we get...
 
\large \tan A \cdot \sec A - \cot A\cdot cosec A = R.H.S.
 

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