Question

cot^2theta-1 =cosec^4theta-2 cosec^2theta​

Answer 1

Step-by-step explanation:

Let theta = A

LHS = cot^4A-1

= (cot^2A)^2 - 1^2

= (cot^2A + 1)(cot^2A - 1)

= cosec^2A(cosec^2A - 1 - 1)

[since 1+cot^2A = cosec^2A which implies cot^2A = cosec^2A-1]

= cosec^2A(cosec^2A - 2)

= cosec^4A - 2cosec^2A

= RHS

Hence proved