Question

prove that tan alpha=sin2alpha/1+cos2alpha and deduce that tan22.5° =√2-1

Answer 1

tan x=sin2x/(1+cos2x)
r.h.s =sin2x/(1+cos2x)
        =2sinx.cosx/(2cos^(x) -1 +a)
       =tanx
l.h.s=r.h.s//
x =22.5
tan(22.5) =sin (2.22.5)/(1+cos(2.22.5))
                 =sin(45)/(1 +cos(45))
                  =1/1+2root2
                  =root2 -1//

Answer 2

Answer:

tanA=sin2A/1+cos2A

tan22.5=√2-1

Step-by-step explanation:

tanA=sin2A/1+cos2A

RHS=sin2A/1+cos2A

=2sinA.cosA/1+2cos^2A-1

=2sinA/2cosA

=tanA

LHS=RHS

tan22.5=√2-1

LHS=√2-1

tan22.5=sin2(22.5)./1+cos2(22.5)

=2sin(22.5).cos2(22.5)/1+2cos^2(22.5)-1

=2sin22.5/2cos22.5

=tan22.5

LHS=RHS