Verified answer

tanx = √2sinx

sinx/cosx = √2 sinx

1/cosx =√2

(1/cosx)^2 = √2^2

1/cos^2(x) = 2

1 + tan^2(x) =2

tan^2(x) = 1

tanx = +/- 1

x= pi/4 +k pi/2

; k is integer

tanx = √2sinx

tanx - √2sinx=0

sinx(1- √2 cosx)=0

sin x=0 => x=0 or 180

cosx = -1/√2 => x=135 and 225

At a stretch x=360 works but it is a repeat of 0

tanx = √2sinx

sinx/cosx = √2sinx

sinx/(cosx * sinx) = √2

1/cosx = √2

sec(x) = √2 = cos(1/√2)

x = asec(√2) = acos(1/√2)

x = 45 degrees

tanx = (sq.rt.2)sinx

tanx = sinx/cosx = (sq.rt.2)sinx

sinx cancels out on both sides:

= 1/cosx = (sq.rt.2)

cross muliply:

=> 1 = (sq.rt.2)cosx

=> 1/(sq.rt.2) = cosx

this gives x as the cosine inverse of 1/(sq.rt.2). i.e.

x = cos^-1[1/(sq.rt.2)]

which gives x = 45 degrees, 315degrees.

tan x = √2 sin x

tan x - √2 sin x = 0

***change tan into sin/cos***

sin x / cos x - √2 sin x = 0

sin x ( 1 / cos x - √2 ) = 0

solve

sin x = 0 AND 1 / cos x - √2 = 0

rewritten as:

sin x = 0 AND cos x = 1/√2