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2Step-by-step explanation:LET THETA = αGiven, SIN α + cosec α = 2=> sinα + 1/sinα = 2=> sin²α + 1 / sinα = 2=> sin²α + 1 = 2sinα=> sin²α - 2sinα + 1 = 0=> ( sinα - 1 )² = 0=> sinα - 1 = 0 => sinα = 1=> cosecα = 1/sinα = 1/1 = 1=> sin^10 α + cosec^10 α = (1)^10 + (1)^10= 1 + 1 = 2



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