Question

If 2 sin α + 3 cos α = 2, then 3 sin α – 2cos α =​

Answer 1

Answer:

+-3

Step-by-step explanation:

Let 3sinα−2cosα=t         ...(1)

Given : 2sinα+3cosα=2         ...(2)

⟹(3sinα−2cosα)  

2

+(2sinα+3cosα)  

2

=t  

2

+2  

2

 

⟹9sin  

2

α−12sinαcosα+4cos  

2

α+4sin  

2

α+12sinαcosα+9cos  

2

α=t  

2

+4

⟹13(sin  

2

α+cos  

2

α)=t  

2

+4

⟹  t  

2

=9

⟹  

t=±3

​