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Solve the trigonometric equation $\frac{1-\sin\left(t\right)}{\cos\left(t\right)}+\frac{-\cos\left(t\right)}{1-\sin\left(t\right)}=2\sec\left(t\right)$

Step-by-step Solution

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Solution

Final answer to the problem

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

$\frac{1-\sin\left(t\right)}{\cos\left(t\right)}+\frac{-\cos\left(t\right)}{1-\sin\left(t\right)}-2\sec\left(t\right)=0$

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$\frac{1-\sin\left(t\right)}{\cos\left(t\right)}+\frac{-\cos\left(t\right)}{1-\sin\left(t\right)}-2\sec\left(t\right)=0$

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Learn how to solve problems step by step online. Solve the trigonometric equation (1-sin(t))/cos(t)+(-cos(t))/(1-sin(t))=2sec(t). Move everything to the left hand side of the equation. The least common multiple (LCM) of a sum of algebraic fractions consists of the product of the common factors with the greatest exponent, and the uncommon factors. Obtained the least common multiple (LCM), we place it as the denominator of each fraction, and in the numerator of each fraction we add the factors that we need to complete. Simplify the numerators.

Final answer to the problem

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

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Function Plot

Plotting: $\frac{1-\sin\left(t\right)}{\cos\left(t\right)}+\frac{-\cos\left(t\right)}{1-\sin\left(t\right)}-2\sec\left(t\right)$

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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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