Simplify the trigonometric expression sin(x)^2cos(x)^5

 Exercise

$\sin^2\left(x\right)\cos^5\left(x\right)$

 

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

$\left(1-\cos\left(x\right)^2\right)\cos\left(x\right)^5$

 Why is 1 - cos(x)^2 = sin(x)^2 ?

 

Multiply the single term $\cos\left(x\right)^5$ by each term of the polynomial $\left(1-\cos\left(x\right)^2\right)$

$\cos\left(x\right)^5-\cos\left(x\right)^2\cos\left(x\right)^5$

 

When multiplying exponents with same base we can add the exponents

$\cos\left(x\right)^5-\cos\left(x\right)^{7}$

$\cos\left(x\right)^5-\cos\left(x\right)^{7}$

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