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Solve the trigonometric equation $\sin\left(x\right)\cos\left(2x\right)+\cos\left(x\right)\sin\left(2x\right)=0$

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Solution

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Final Answer

$x=0+2\pi n,\:x=\frac{1}{3}\pi+\frac{2}{3}\pi n\:,\:\:n\in\Z$
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Step-by-step Solution

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1

Simplify using the identity for the sine of a sum, in reverse: $\sin(\alpha)\cos(\beta)\pm\cos(\alpha)\sin(\beta)=\sin(\alpha\pm \beta)$, where the angle $\alpha$ equals $x$, and the angle $\beta$ equals $2x$

$\sin\left(x+2x\right)=0$

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$\sin\left(x+2x\right)=0$

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Learn how to solve trigonometric equations problems step by step online. Solve the trigonometric equation sin(x)cos(2x)+cos(x)sin(2x)=0. Simplify using the identity for the sine of a sum, in reverse: \sin(\alpha)\cos(\beta)\pm\cos(\alpha)\sin(\beta)=\sin(\alpha\pm \beta), where the angle \alpha equals x, and the angle \beta equals 2x. Combining like terms x and 2x. The angles where the function \sin\left(3x\right) is 0 are. Solve the equation (1).

Final Answer

$x=0+2\pi n,\:x=\frac{1}{3}\pi+\frac{2}{3}\pi n\:,\:\:n\in\Z$

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Function Plot

Plotting: $\sin\left(x\right)\cos\left(2x\right)+\cos\left(x\right)\sin\left(2x\right)$

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0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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Similar Problems Solved

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$\csc\left(x\right)+\sin\left(x\right)=\cot\left(x\right)\cdot\cos\left(x\right)$

$\ln\left(\frac{1}{x}\right)+\ln\left(2x^3\right)=\ln\left(486\right)-\ln\left(3\right)$

$\frac{\sec\left(x\right)-1}{1-\cos\left(x\right)}=\sec\left(x\right)$

Main Topic: Trigonometric Equations

A trigonometric equation is an equation in which one or more trigonometric ratios appear.

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