Question

If Sin 0 + Cosec 0 =3, then find the value of Sin^4 +1/sin^2​

Answer 1

Given:

sin X + cosec X = 3 ——> 1

(sin^4 X + 1)/sin^2 X

= (sin^4 X/sin^2 X) + (1/sin^2 X)

= sin^2 X + cosec^ X

= (sin^2 X + cosec^ X + 2sin X*cosec X) - 2sin X*cosec X

= (sin X + cosec X)^2 + 2*sinx/sinx

= (sin X + cosec X)^2 + 2

= 3^2 + 2 [ From 1 ]

= 9 + 2

= 11 ——> Answer