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Step-by-step Solution

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

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Step-by-step explanation

Problem to solve:

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

Learn how to solve simplify trigonometric expressions problems step by step online.

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

Unlock this full step-by-step solution!

Learn how to solve simplify trigonometric expressions problems step by step online. Simplify the trigonometric expression 1/(sin(2*x)^2cos(2*x)^4). Using the sine double-angle identity. The power of a product is equal to the product of it's factors raised to the same power. The power of a product is equal to the product of it's factors raised to the same power. Applying an identity of double-angle cosine: \cos(2\theta)=\cos(\theta)^2-\sin(\theta)^2.

Answer

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

Problem Analysis

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

Time to solve it:

~ 0.85 seconds