Question

prove that- cosec^4 A-cosec^2 A=cot^4 A+cot^2 A

Answer 1

$take \: the \:lhs \\ \\ (cot {}^{2} a + 1) {}^{2} - (1 + cot {}^{2}a) \\ cot {}^{4} a + 1 + 2cot {}^{2} a - 1 - cot {}^{2} a \\ cot {}^{4} a + cot {}^{2}a = rhs$

Answer 2

Answer:

cosec⁴A-cosec²A=cot⁴A-cot²A

Step-by-step explanation:

LHS = cosec⁴A-cosec²A

Take cosec²A common in each term, we get

= cosec²A(cosec²A-1)

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We know the Trigonometric identity:

Cosec²A = 1+ cot²A

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= (1+cot²A)[1+cot²A-1]

= (1+cot²A)(cot²A)

= cot⁴A-cot²A

= RHS

Therefore,

cosec⁴A-cosec²A=cot⁴A-cot²A

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