Question

7. If Sin x + cosec x = 2, then Sin 2x + cosec 2x
​

Answer 1

sin X + (1/sin X ) = 2

sin ^2 X + 1 = 2 sin X

put sin X = y then

y^2 + 1 = 2y

y^2 - 2y+1 = 0

y^2-y-y+1 = 0

y(y-1) -1(y-1)= 0

(y-1)(y-1) = 0

y = 1

sin X = 1

cosec X = 1

sin^n X + cosec ^n X = (1)^n + ( 1)^n = 2