Question

(Cot +cosec)×(cot-cosec)=

Answer 1

$Value \: of \: (cot A + cosecA)( cotA - cosecA )\\= cot^{2} A - cosec^{2} A$

/* By Algebraic Identity */

$\boxed { \pink { (x+y)(x-y) = x^{2} - y^{2} }}$

$= -1$

/* By Trigonometric Identity */

$\boxed { \pink { cot^{2}A + 1 = cosec^{2} A }}$

Therefore.,

$\red{Value \: of \: (cot A + cosecA)( cotA - cosecA )} \green {= -1}$

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