Question

cot 4 degree A-1=cosec 4 degree A - 2cosec2degreeA​

Answer 1

Answer:

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

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

$= cosec^{2} A ( cosec^{2}A-1-1)\\=cosec^{2}A(cosec^{2}A - 2)\\= cosec^{4}A - 2cosec^{2}A\\=RHS$

$Hence, proved$

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