Question #6a844

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Question #6a844

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Answer 1 · 2017-02-25T03:05:30

$x = \frac{3 π}{2}, \frac{π}{10}, \frac{π}{2} when x \in [0.2 π]$ $x=(3pi)/2,pi/10,pi/2" when "x in [0.2pi]$

Explanation:

$sin 2 x - cos 3 x = 0$ $sin2x-cos3x=0$

$\Rightarrow sin 2 x - sin (\frac{π}{2} - 3 x) = 0$ $=>sin2x-sin(pi/2-3x)=0$

$\Rightarrow 2 cos (\frac{1}{2} (2 x + \frac{π}{2} - 3 x)) sin (\frac{1}{2} (2 x - \frac{π}{2} + 3 x)) = 0$ $=>2cos(1/2(2x+pi/2-3x))sin(1/2(2x-pi/2+3x))=0$

$\Rightarrow cos (\frac{x}{2} - \frac{π}{4}) sin (\frac{5 x}{2} - \frac{π}{4}) = 0$ $=>cos(x/2-pi/4)sin((5x)/2-pi/4)=0$

when

$cos (\frac{x}{2} - \frac{π}{4}) = 0 = cos (\frac{π}{2}) = cos (\frac{3 π}{2})$ $cos(x/2-pi/4)=0=cos(pi/2)=cos ((3pi)/2)$

$cos (\frac{x}{2} - \frac{π}{4}) = 0 = cos (\frac{π}{2})$ $cos(x/2-pi/4)=0=cos(pi/2)$

$\Rightarrow cos (\frac{x}{2} - \frac{π}{4}) = cos (\frac{π}{2})$ $=>cos(x/2-pi/4)=cos(pi/2)$

$\Rightarrow \frac{x}{2} = \frac{π}{2} + \frac{π}{4} = \frac{3 π}{4}$ $=>x/2=pi/2+pi/4=(3pi)/4$

$\Rightarrow x = \frac{3 π}{2}$ $=>x=(3pi)/2$

Again

$cos (\frac{x}{2} - \frac{π}{4}) = cos (\frac{3 π}{2})$ $cos(x/2-pi/4)=cos ((3pi)/2)$

$\Rightarrow \frac{x}{2} - \frac{π}{4} = \frac{3 π}{2}$ $=>x/2-pi/4=(3pi)/2$

$\Rightarrow x = 3 π + \frac{π}{2} > 2 π not wanted$ $=>x=3pi+pi/2>2picolor(red)" not wanted"$

when

$sin (\frac{5 x}{2} - \frac{π}{4}) = 0 = sin 0 = sin (π)$ $sin((5x)/2-pi/4)=0=sin0=sin(pi)$

$\Rightarrow \frac{5 x}{2} - \frac{π}{4} = 0$ $=>(5x)/2-pi/4=0$

$\Rightarrow x = \frac{π}{4} \times \frac{2}{5} = \frac{π}{10}$ $=>x=pi/4xx2/5=pi/10$

Again

$sin (\frac{5 x}{2} - \frac{π}{4}) = sin (π)$ $sin((5x)/2-pi/4)=sin(pi)$

$\Rightarrow \frac{5 x}{2} = π + \frac{π}{4} = \frac{5 π}{4}$ $=>(5x)/2=pi+pi/4=(5pi)/4$

$\Rightarrow x = \frac{π}{2}$ $=>x=pi/2$

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Question #6a844

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