Question

Cosec⁴A - cot²A= cos²A + cos⁴A

Answer 1

Step-by-step explanation:

TO PROVE:- cosec^4-cot^2= cosec^2+cot^4

PROVE:-  

   LHS= cosec^4-cot^2

      =   (cosec^2)^2-cot^2

  =    [ using; cosec^2 = 1+cot^2]

  =  (1+cot^2)^2-cot^2

  =  1+cot^4+2cot^2-cot^2

   = 1+cot^4+cot^2

   = 1+cot^2+cot^4

      [putting 1+cot^2= cosec^4]

   = cosec^4+cot^2

    =RHS

    LHS=RHS

HENCE PROVED