How to approach this

Question

If $2 sin\alpha + 15 cos \alpha = 7$

 

find $cot \alpha$

 

?

Answer 1

 

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