Respuesta :
Answer:
Step-by-step explanation:
cos x cos (3x)+sinx sin (3x)=0
cos (x-3x)=0
cos(-2x)=0
cos 2x=0=cos (2n+1)π/2
where n=0,1,2,3∞∞∞∞
2x=(2n+1)π/2
x=(2n+1)π/4
put n=0,1,2,3
x=π/4,3π/4,5π/4,7π/4
The solution of equation cos(x) cox(3x) + sin(x) sin(3x) = 0 are [tex]\bold{x=\frac{\pi}{4},~\frac{3\pi}{4}}[/tex]
What is equation?
It is a mathematical statement which consists of equal symbol between two algebraic expressions."
Formula for cos(A - B):
cos(A - B) = cos(A)cos(B) + sin(A)sin(B)
For given question,
We have been given an equation cos x cox(3x)+sin x sin(3x)=0 .............(i)
We know, cos(A - B) = cos(A)cos(B) + sin(A)sin(B)
So, cos x cox(3x) + sin x sin(3x) = cos(x - 3x)
So, the equation (i) becomes,
⇒ cos(x - 3x) = 0
⇒ cos(-2x) = 0 ..................(ii)
We know, for any angle m,
cos(-m) = cos(m)
⇒ cos(-2x) = cos(2x)
So the equation (ii) would be,
cos(2x) = 0
We know, in the interval [0, 2π]
cos([tex]\frac{\pi}{2}[/tex]) = 0 and cos([tex]\frac{3\pi}{2}[/tex]) = 0
This means, [tex]2x=\frac{\pi}{2}[/tex] or [tex]2x=\frac{3\pi}{2}[/tex]
⇒ [tex]x = \frac{\pi}{4}[/tex] or [tex]x=\frac{3\pi}{4}[/tex]
Therefore, the solution of equation cos(x) cox(3x)+sin(x) sin(3x)=0 are [tex]\bold{x=\frac{\pi}{4},~\frac{3\pi}{4}}[/tex]
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