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Simplify the trigonometric expression $\frac{\cos\left(a\right)^2}{\sin\left(a\right)\left(1-\sin\left(a\right)\right)}$

Step-by-step Solution

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Final answer to the problem

$\frac{1}{-\sec\left(a\right)^2+1+\sqrt{\sec\left(a\right)^2-1}\sec\left(a\right)}$
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Step-by-step Solution

How should I solve this problem?

  • Express in terms of Secant
  • Find the derivative
  • Integrate using basic integrals
  • Verify if true (using algebra)
  • Verify if true (using arithmetic)
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
  • Integrate by parts
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1

Multiply the single term $\sin\left(a\right)$ by each term of the polynomial $\left(1-\sin\left(a\right)\right)$

$\frac{\cos\left(a\right)^2}{\sin\left(a\right)-\sin\left(a\right)^2}$

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$\frac{\cos\left(a\right)^2}{\sin\left(a\right)-\sin\left(a\right)^2}$

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Learn how to solve problems step by step online. Simplify the trigonometric expression (cos(a)^2)/(sin(a)(1-sin(a))). Multiply the single term \sin\left(a\right) by each term of the polynomial \left(1-\sin\left(a\right)\right). Apply the trigonometric identity: \sin\left(\theta \right)=\frac{\sqrt{\sec\left(\theta \right)^2-1}}{\sec\left(\theta \right)}, where x=a. Combine \frac{\sqrt{\sec\left(a\right)^2-1}}{\sec\left(a\right)}-\sin\left(a\right)^2 in a single fraction. Divide fractions \frac{\cos\left(a\right)^2}{\frac{\sqrt{\sec\left(a\right)^2-1}-\sin\left(a\right)^2\sec\left(a\right)}{\sec\left(a\right)}} with Keep, Change, Flip: a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}.

Final answer to the problem

$\frac{1}{-\sec\left(a\right)^2+1+\sqrt{\sec\left(a\right)^2-1}\sec\left(a\right)}$

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Function Plot

Plotting: $\frac{1}{-\sec\left(a\right)^2+1+\sqrt{\sec\left(a\right)^2-1}\sec\left(a\right)}$

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6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
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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