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Solve the trigonometric equation $\cot\left(x\right)+2\sin\left(x\right)=\csc\left(x\right)\sec\left(x\right)+\tan\left(x\right)$

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Solution

Final answer to the problem

$x=0+\pi n,\:x=\pi+\pi n,\:x=0+2\pi n,\:x=2\pi+2\pi n\:,\:\:n\in\Z$
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Step-by-step Solution

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  • Express in terms of sine and cosine
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Move everything to the left hand side of the equation

$\cot\left(x\right)+2\sin\left(x\right)-\csc\left(x\right)\sec\left(x\right)-\tan\left(x\right)=0$

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$\cot\left(x\right)+2\sin\left(x\right)-\csc\left(x\right)\sec\left(x\right)-\tan\left(x\right)=0$

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Learn how to solve problems step by step online. Solve the trigonometric equation cot(x)+2sin(x)=csc(x)sec(x)+tan(x). Move everything to the left hand side of the equation. Applying the tangent identity: \displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}. Applying the trigonometric identity: \cot\left(\theta \right) = \frac{\cos\left(\theta \right)}{\sin\left(\theta \right)}. Applying the cosecant identity: \displaystyle\csc\left(\theta\right)=\frac{1}{\sin\left(\theta\right)}.

Final answer to the problem

$x=0+\pi n,\:x=\pi+\pi n,\:x=0+2\pi n,\:x=2\pi+2\pi n\:,\:\:n\in\Z$

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Function Plot

Plotting: $\cot\left(x\right)+2\sin\left(x\right)-\csc\left(x\right)\sec\left(x\right)-\tan\left(x\right)$

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7
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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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