Sum of all tanx values

Question

0<x<90
2sin²x-2sin2x+4cos²x=1
Sum of all tanx values

Answer 1

rYou question is not well-specified. But anyway,

2sin²x-2sin2x+4cos²x=1 (divide both sides by cos²(x))

2tan²(x)-4tan(x)+1=1+tan²(x)

tan²(x)-4tan(x)=0

tan(x)(tan(x)-4)=0

tan(x)=0 or /and tan(x)=4

Solve this equation  for 0<x<90

 

Answer 2

2sin² x - 2sin 2x + 4cos² x = 1

2sin² x - 2(2 sin x cos x) + 4cos² x = 1

 

Can you simplify and use the zero product rule?