Question

cosec4A- cot 4A= cosec2A + cot2A
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Answer 1

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