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# Truth set of x ?

Find the truth set given that sinx° = sin2x if 0<=x°<=360°

### 2 Answers

Relevance
• sin2x = 2sinxcosx

so, sinx = 2sinxcosx

i.e. 2sinxcosx - sinx = 0

or, sinx(2cosx - 1) = 0

Hence, sinx = 0 or cosx = 1/2

Then, x = 360n°, 180 + 360n°, 60° + 360n° or -60 + 360n°...for n = 0, 1, 2,...

so, x = 0°, 60°, 180° and 300°...for 0° ≤ x ≤ 360°

Note: I've never heard of the 'truth' or 'false' set before!!

:)>

• One method :

sin(x) = sin(2x)

sin(x) = sin(x+x)

sin(x) = 2sin(x)cos(x)

sin(x)(1 - 2cos(x)) = 0

case1. sin(x) = 0

x = 0° or 180° or 360°

case2. cos(x) = 1/2

x = 60° or 300°

Another method：

sin(x) = sin(2x)

case1. x + 360n = 2x (n:integer)

-x = -360n

x = 360n so x = 0° or 360°

case2. x + 360n = 180 - 2x (n:integer)

3x = 180 - 360n

x = 60 - 120n so x = 60° or 180° or 300°

The truth set is {0°,60°,180°,300°,360°}

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