Question

sin 2x=sinx

Answer 1

if sin 2x=sin x then 2x=x must be true as well

2x=x for only which number is true?

Answer 2

(subtract x from both sides)

Answer 3

i think it should
sin x = tan x.cos x

Answer 4

to find all the solutions , you should use
sin 2x = 2 sin(x) cos(x)

and solve
2 sin(x) cos(x) = sin(x)
or
2 sin(x) cos(x) - sin(x) = 0

Answer 5

ok thanks phi^^

Answer 6

@phi sinx=2sinx cosx. can u explain me why?

Answer 7

sin(2x) = 2 sinx cosx

substitute into
sin 2x=sinx
to get
2 sinx cosx = sinx

Answer 8

to solve:
2 sinx cosx = sinx
2 sinx cosx - sinx = 0
factor out a sinx
sinx (2 cosx -1) = 0

that means either sinx =0 or 2cosx -1 = 0
sinx=0 has solutions 0, pi, 2pi, or in general ±k pi , k an integer
2cosx -1 =0
cosx = 1/2
x = 60º or 300º

Answer 9

why? sin 2x= 2 sinx cosx. i don't understood :( sorry

Answer 10

do you know the sum of angles formula?
sin(a+b)= sin(a) cos(b) + cos(a) sin(b)

Answer 11

with a=b it gives you
sin(a+a) = sin(a) cos(a) + cos(a) sin(a) or
sin(2a) = sin(a)+cos(a) + sin(a)cos(a)
sin(2a) = 2 sin(a) cos(a)

Answer 12

thx a lot^^

Answer 13

Here is a derivation of the sin(x+y)
http://www.jimloy.com/geometry/trigz.htm