Question

prove that sin^2/cos^2 + cos^2/sin^2 = sec^2 - cosec^2 - 2

Answer 1

Answer:

Step-by-step explanation:I think u need to check the question again regarding the signs

Answer 2

Answer:

Step-by-step explanation:

Note:Your question is actually not right at the RHS because its should be sec^2.cosec^2 - 2 and not sec^2 - Cosec^2 - 2

Now,

       Sin^2/Cos^2 + Cos^2/Sin^2
       Sin^4 + Cos^4/ (Cos^2)(Sin^2)

       (Sin^2 + Cos^2)^2 - 2Sin^2.Cos^2/Cos^2.Sin^2 [Since:(Sin + Cos)^2 =  

                                                                                      Sin^2+Cos^2+2SinCos]

       (Sin^2 + Cos^2)^2/Cos^2.Sin^2 - 2Sin^2.Cos^2/Cos^2.Sin^2

       1/Cos^2.Sin^2 - 2 [Since:Sin^2 + Cos^2 = 1]

       Sec^2.Cosec^2 - 2 = RHS Proved