Simplify the trigonometric expression cos(x)sin(x)^2

 Exercise

$cos\left(x\right)\cdot sen^2\left(x\right)$

 

Applying the trigonometric identity: $\sin\left(\theta \right)^2 = 1-\cos\left(\theta \right)^2$

$\cos\left(x\right)\left(1-\cos\left(x\right)^2\right)$

 Why is 1 - cos(x)^2 = sin(x)^2 ?

 

Multiply the single term $\cos\left(x\right)$ by each term of the polynomial $\left(1-\cos\left(x\right)^2\right)$

$\cos\left(x\right)-\cos\left(x\right)^2\cos\left(x\right)$

 

When multiplying exponents with same base you can add the exponents: $-\cos\left(x\right)^2\cos\left(x\right)$

$\cos\left(x\right)-\cos\left(x\right)^{3}$

$\cos\left(x\right)-\cos\left(x\right)^{3}$

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