Question

show that (cotA-1+cosecA) /(CotA+1-cosecA)=cotA+cosecA​

Answer 1

Answer:

ey Friend :-)

Here is your answer

=> 1 / (cosecA - cotA) . . . . . . . . . . .multiply top & bottom by (cosecA + cotA)  

=> (cosecA + cotA) /(cosec^2A - cot^2A) . . . . . . .use cosec^2A = 1 +                                                                                                                        cot^2A  

=> (cosecA +cotA) / 1  

=> cosecA + cotA

RHS = LHS  

Hence, proofed.

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Answer 2

$\huge\boxed{\underline{\underline{\green{\tt Solution}}}} </p><p>$

$\displaystyle \: \frac{CotA - 1 + CosecA}{CotA + 1 - CosecA}$

$= \displaystyle \: \frac{CotA + CosecA - 1}{CotA - CosecA + 1}$

$= \displaystyle \: \frac{CotA + CosecA - ( {Cosec}^{2}A - {Cot}^{2}A) }{CotA + 1 - CosecA}$

$=\frac{(CotA + CosecA )-(CosecA + CotA )(CosecA - CotA ) }{CotA + 1 - CosecA}$

$= \frac{(CotA + CosecA )(CotA + 1 - CosecA)}{(CotA + 1 - CosecA)}$

$= (CotA + CosecA)$