# Step-by-step Solution

## Simplify $\frac{1}{\sin\left(2x\right)^2\cos\left(2x\right)^4}$

Go
1
2
3
4
5
6
7
8
9
0
x
y
(◻)
◻/◻
2

e
π
ln
log
lim
d/dx
Dx
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

### Videos

$\csc\left(x\right)^2\frac{1}{\left(1-2\sin\left(x\right)^2\right)^4}\cdot\frac{\frac{1}{4}}{\cos\left(x\right)^2}$

## Step-by-step explanation

Problem to solve:

$\left(1/\left(sin\left(2\cdot x\right)^2\cdot cos\left(2\cdot x\right)^4\right)\right)$
1

Using the sine double-angle identity

$\frac{1}{\left(2\sin\left(x\right)\cos\left(x\right)\right)^2\cos\left(2x\right)^4}$
2

Applying an identity of double-angle cosine

$\frac{1}{\left(2\sin\left(x\right)\cos\left(x\right)\right)^2\left(1-2\sin\left(x\right)^2\right)^4}$

$\csc\left(x\right)^2\frac{1}{\left(1-2\sin\left(x\right)^2\right)^4}\cdot\frac{\frac{1}{4}}{\cos\left(x\right)^2}$
$\left(1/\left(sin\left(2\cdot x\right)^2\cdot cos\left(2\cdot x\right)^4\right)\right)$

~ 0.66 seconds

### Struggling with math?

Access detailed step by step solutions to millions of problems, growing every day!