Question

If sin x + cosec x = 2 then sin^n x + cosec^n x =?

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

Answer 2

Answer:

2

Step-by-step explanation:

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

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