Question

(1-cos2A)÷sin2A=tan2A

Answer 1

(1) If you mean (1-cos(2A))÷sin(2A)=tan(2A) then:

since cos(2A)=1-2sin²(A) and sin(2A)=2sin(A)cos(A):

2sin²(A)/(2sin(A)cos(A))=sin(A)/cos(A)=tan(A).

So tan(A)=tan(2A).

Therefore A=2A⇒A=0. More generally A=nπ where n is an integer.

(2) If you mean (1-cos²(A))÷sin²(A)=tan²(A) then:

sin²(A)/sin²(A)=1=tan²(A), tan(A)=±1, A=±π/4, or more generally (2n+1)π/4, for integer n.