Question

Cotx - 2sin2x = 1 solve the equation

Answer 1

We know sin 2x=2sin x cos x  

cot x-4 cos x sin x=1  

Let y=cot x  

cot x- 4sin xcos x=>cot x((cot x)²-3)/(1+cot² x)  

y(y²-3)/(y²+1)=1  

Multiplying y²+1 both side  

y(-3+y²)=1+y²  

-3y+y^3=1+y²  

(1+y)(-1-2y+y²)=0  

1+y=0  

-1-2y+y²=1  

y=-1  

cot x=-1  

Using inverse cotangent of both side  

x=-π/4+πn ,n belongs toZ  

There for  

x=-π/4+πn  

x=cot^-1(1+√2)+πn  

x=cot^-1(1-√2)+πn  

Where n belongs to Z

Answer 2

scene is the answer given by first