Question

If cosecA+cotA=x then find cosecA-cotA

Answer 1

Answer:

cosecA + cotA = x

=> 1/(cosecA + cotA) = 1/x

=>( cosecA - cotA) /(cosecA+cotA)(cosecA-cotA) = 1/x

=> (cosecA-cotA) /(cosec²A-cot²A) = 1/x

=>(cosecA-cotA) / 1 = 1/x

=> cosecA-cotA = 1/x

Answer 2

$Given \:cosec A + cot A = x \:--(1)$

/* Multiplying both sides of the equation by

(cosec A - cot A ), we get */

$\implies (cosec A + cot A )(cosec A - cot A )\\= x(cosec A - cot A )$

$\implies cosec^{2} A - cot^{2} A = x (cosec A - cot A )$

$\implies 1 = x (cosec A - cot A )$

$\implies \frac{1}{x} = cosec A - cot A$

Therefore.,

$\red { cosec A - cot A }\green {= \frac{1}{x}}$

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