Question

prove that sin/tan+cosec=2+sin/tan-cosec

Answer 1

cosec^2 51 = sin^2 51 = cos^2 39.

1/ cosec^2 51 +sin^2 39 = cos^2 39 +sin^2 39 = 1.

sec^2 39 = 1/ cos^2 39 = 1/ sin^2 51

sin^2 51* sec^2 39 = 1 .

1/ cosec^2 51 +sin^2 39 - 1 /sin^2 51* sec^2 39 = 0

Hence the given expression is tan^2 51 = ( cot 39) ^2 =( cosec 39/ sec 39)^2

(cosec 39) ^ 2 = x^2

(sec 39) ^2 = (1- x^2)

(tan 51) ^2 = x^ 2 / ( 1-x^2)

Hence the given expression is x^ 2 / ( 1-x^2)