Question

51. If cosec 39° = p, then the value of
1
+ sin2 39° + tan2 51°-
cosec? 51°
1
sin? 51°.sec 39°
is ....
(2)​

Answer 1

Step-by-step explanation:

cosec 39

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

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

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