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we have 2sinα+15cosα=7

divide both side by sinα in order to get cotα term, we get 

         2+ 15cotα = 7cosecα  (as cosec2α =1+cot2α)

         2+ 15cotα= 7( 1+cot2α)1/2 

         4+60cotα+ 225cot2α= 49(1+ cot2α)

         176cot2α + 60cotα-45=0

now u can use quadratic equation to find the value of cotα that is .

        = -0.704 and 0.363

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