Question

prove that tan15°+cot15°=4

Answer 1

hey there,

Let α = 15°, then we have the LHS =

tan(α) + cot(α) =

sin(α)/cos(α) + cos(α)/sin(α) =

{sin^2(α) + cos^2(α)} / (sin(α).cos(α)} =

1 / (sin(α).cos(α)} =

2 / (2.sin(α).cos(α)} =

2 / (sin(2α)} =

2 / (1/2} =     (since α = 15°, and sin(30) = ½)

4 = RHS

Hope this Helps!