can I please have help with these 3 questions?

Question

1. Solve this equation graphically on the interval [0, 2ð]. list the solutions.

sin(2x)-1=tan x

2. solve sin x cos x= sqrt3/4
3. solve tan^2 x-3tan x+2=0

thank you! show step by step please.

Answer 1

1. try
http://www.wolframalpha.com/input/?i=sin%282x%29-1%3Dtan%28x%29+

2.
sinxcosx = √3/4
times 2
2sinxcosx = √3/2
sin(2x) = √3/2
2x = 60° or 2x = 120°
x = 30° or x = 60°
period of sin 2x is 180°
so other solutions
x = 30 + k(180) and x = 60 + k(180) degrees , where k is an inter

in radians:
x = π/6 + kπ or x = π/3 + kπ

3. let tanx = t
you have t^2 - 3t + 2 = 0
(t-2)(t-1) = 0
t = 2 or t = -1
so
tanx = 2 -----> two answers in domain 0≤x≤2π
or
tanx = -1 ---> two answers in domain 0 ≤ x ≤ 2

give it a try

Answer 2

thank you so much!