Question

Sec(x)+ cosec(x) = 1 then find sin2(x)​

Answer 1

Given,

sin x + cosec x = 2

sin x + (1/sin x) = 2

(sin2x + 1)/sin x = 2

sin2x + 1 = 2 sin x

sin2x – 2 sin x + 1 = 0

(sin x – 1)2 = 0

sin x – 1 = 0

sin x = 1

cosec x = 1/sin x = 1

sinnx + $\sf{cosec^n}$x = (1)n + (1)n

= 1 + 1

= 2