Question

Prove that cot raised to 4 minus 1 is equal to cosec raise to 4 - 2 cosec square A

Answer 1

Answer:

cot⁴A-1=cosec⁴A-2cosec²A

cos⁴A/sin⁴A - sin⁴A/sin⁴A = 1/sin⁴A - 2sin²A/sin⁴A

cos⁴A-sin⁴A=1-2sin²A

(cos²A+sin²A)(cos²A-sin²A)=cos²A+sin²A-2sin²A

cos²A-sin²A=cos²A-sin²A

Thus  proved.