Question

If cosecA - cosec²A +1 = 0 , find the value of the expression cot⁴A - cot²A.​

Answer 1

Answer:

1

Step-by-step explanation:

we know

1 + cot²A = cosec²A

To find

cot⁴A - cot²A

given

cosecA -cosec²A + 1 = 0

*putting the value of cosec²A = 1 + cot²A

and

cosecA = √ ( 1 + cot²A)

√ ( 1 + cot²A) - 1 - cot²A + 1 = 0

√ ( 1 + cot²A) - cot²A = 0

√ ( 1 + cot²A) = cot²A

squaring both side

(√ ( 1 + cot²A))² = (cot²A)²

1 + cot²A = cot⁴A

cot⁴A - cot²A = 1

so the answer is 1