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