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Solve the trigonometric equation $\tan\left(t\right)+\cos\left(t\right)\csc\left(t\right)=\sec\left(t\right)\csc\left(t\right)+\cot\left(t\right)$

Step-by-step Solution

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Solution

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Final answer to the problem

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

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  • Express in terms of sine and cosine
  • Simplify
  • Simplify into a single function
  • Express in terms of Sine
  • Express in terms of Cosine
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  • Express in terms of Cotangent
  • Express in terms of Secant
  • Express in terms of Cosecant
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Simplify $\cos\left(t\right)\csc\left(t\right)$ into $\cot(t)$ by applying trigonometric identities

Learn how to solve quotient rule of differentiation problems step by step online.

$\tan\left(t\right)+\cot\left(t\right)=\sec\left(t\right)\csc\left(t\right)+\cot\left(t\right)$

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Unlock the first 3 steps of this solution

Learn how to solve quotient rule of differentiation problems step by step online. Solve the trigonometric equation tan(t)+cos(t)csc(t)=sec(t)csc(t)+cot(t). Simplify \cos\left(t\right)\csc\left(t\right) into \cot(t) by applying trigonometric identities. Move everything to the left hand side of the equation. Cancel like terms \cot\left(t\right) and -\cot\left(t\right). Applying the cosecant identity: \displaystyle\csc\left(\theta\right)=\frac{1}{\sin\left(\theta\right)}.

Final answer to the problem

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

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Function Plot

Plotting: $\tan\left(t\right)+\cos\left(t\right)\csc\left(t\right)-\sec\left(t\right)\csc\left(t\right)-\cot\left(t\right)$

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0
a
b
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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

How to improve your answer:

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Main Topic: Quotient Rule of Differentiation

The quotient rule is a formal rule for differentiating problems where one function is divided by another.

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