Question

Solve the following equations for 0 < x < 2pi

A) sin^2x=2sinxcosx

B) 3tanx=cosx

Please help
Thankyou

Answer 1

A

x = 0 is a solution
also
sin x = 2 cos x
is
tan x = 2
that happens at x = 63.4 degrees and at x = 243.4 degrees
convert those to radians by multiplying by pi/180

Answer 2

B
3 (sin x/ cos x) = cos x
3 sin x = cos^2 x

3 sin x = (1 - sin^2 x)

sin^2 x + sin x -1 = 0

let z = sin x

z^2 + z - 1 = 0

z = [ -1 +/- sqrt (1+4) ]/2

z = [-1 +/- 2.24 ]/2

z = sin x = .618 or something too big to be a sin of anything