Question

the value of cosec^4A - 2 cosec^2A +1 is​

Answer 1

Step-by-step explanation:

cosec^4 A - 2 cosec^2A +1

= (cosec^2A-1)^2

=( cot^2A)^2 {since ,cosec^2A- cot^2A=1}

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Answer 2

Step-by-step explanation:

We are going to use one of the the written identities in solving the question .

1) sin ^2 theta + cos ^2 theta = 1

2) sec ^2 theta - tan ^2 theta = 1

3) cosec ^2 theta - cot ^2 theta = 1

Let us assume that a = cosec ^2 A and b = 1 .

We know that , ( a + b ) ^2 = a^2 + b^2 + 2 a b

Cosec⁴A - 2Cosec²A + 1

(Cosec²A - 1)²

(Cot²A)²

Cot⁴A

Hence the required answer is cot ^4 A ..