If sin x + csc x = 2,then sin^n x + csc^n x i | vedclass

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(A) Given the equation: $\sin x + \csc x = 2$.Since $\csc x = \frac{1}{\sin x}$,we can write the equation as $\sin x + \frac{1}{\sin x} = 2$.Multiplyi

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$2$

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(A) Given the equation: $\sin x + \csc x = 2$.Since $\csc x = \frac{1}{\sin x}$,we can write the equation as $\sin x + \frac{1}{\sin x} = 2$.Multiplying by $\sin x$,we get $\sin^2 x + 1 = 2 \sin x$,which simplifies to $\sin^2 x - 2 \sin x + 1 = 0$.This is a perfect square: $(\sin x - 1)^2 = 0$.Therefore,$\sin x = 1$.Since $\sin x = 1$,then $\csc x = \frac{1}{1} = 1$.Substituting these values into the expression $\sin^n x + \csc^n x$,we get $1^n + 1^n = 1 + 1 = 2$.

If $\sin x + \csc x = 2$,then $\sin^n x + \csc^n x$ is equal to

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