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

Step-by-step Solution

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Solution

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Final Answer

$\sin\left(\theta\right)^2\left(1-\sin\left(\theta\right)^2\right)$
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Step-by-step Solution

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Using the sine double-angle identity: $\sin\left(2\theta\right)=2\sin\left(\theta\right)\cos\left(\theta\right)$

$\frac{1}{4}\left(2\sin\left(\theta\right)\cos\left(\theta\right)\right)^2$
Why does sin(2x) = 2sin(x)cos(x) ?

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

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

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Learn how to solve simplify trigonometric expressions problems step by step online. Simplify the trigonometric expression 1/4sin(2t)^2. Using the sine double-angle identity: \sin\left(2\theta\right)=2\sin\left(\theta\right)\cos\left(\theta\right). The power of a product is equal to the product of it's factors raised to the same power. Any expression multiplied by 1 is equal to itself. Applying the pythagorean identity: \cos^2(\theta)=1-\sin(\theta)^2.

Final Answer

$\sin\left(\theta\right)^2\left(1-\sin\left(\theta\right)^2\right)$

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Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Express in terms of sine and cosineSimplifySimplify into a single functionExpress in terms of CosineExpress in terms of TangentExpress in terms of CotangentExpress in terms of SecantExpress in terms of CosecantFactorFind the derivativeSolve 0.25sin2t^2 using basic integrals

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Plotting: $\sin\left(t\right)^2\left(1-\sin\left(t\right)^2\right)$

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(◻)
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◻/◻
/
÷
◻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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Main Topic: Simplify Trigonometric Expressions

Simplification of trigonometric expressions consists of rewriting an expression with trigonometric functions in a simpler form. To perform this task, we usually use the most common trigonometric identities, and some algebra.

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