Question

cot^4 A-1=cosec4A-2cosecA​

Answer 1

$LHS = cot^{4} A- 1 \\= (cot^{2}A)^{2} - 1^{2} \\= (cot^{2}A + 1)(cot^{2}A -1)$

$\boxed { \pink { Since, a^{2} - b^{2} = ( a + b )( a - b )}}$

$= cosec^{2}A ( cosec^{2} A- 1 - 1 )$

$\boxed { \orange { Since, 1+cot^{2}A = cosec^{2}A }}$

$= cosec^{2}A ( cosec^{2} A- 2)$

$= cosec^{4} A - 2cosec^{2} A$

$= RHS$

$Hence, Proved.$

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Answer 2

cot⁴A - 1

(cot²A)²-1²

(cot²A+1)(cot²A-1)

(cosec²A-1+1)(cosec²A-1-1)

cosec²A(cosec²A-2)

cosec²A-2cosec²A

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