Question

Solve equation for A,
Cos²A/cot²A-cos²A =3

Answer 1

This problem has no solution. Because if we simplify it we get cos2A = -3 which is not possible for any value of A as -1<=cos@<=1

Answer 2

   Cos²A             = 3

cot²A-cos²A

⇒           Cos²A                = 3

  (cos²A/sin²A)-cos²A

⇒        Cos²A                = 3

  cos²A[(1/sin²A)-1]

⇒       1             = 3

  (1/sin²A)-1

⇒  Sin²A     = 3

    1-sin²A

⇒  Sin²A     = 3

    Cos²A

⇒  Tan²A      = 3

⇒Tan A = √3

We know that,

Tan 60° = √3

∴, A = 60°

Hope it help....