Simplify the trigonometric expression 2sin(60)^2tan(30)

 Exercise

$2sin^2\left(60\right)\cdot tan\left(30\right)$

 

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

$2\left(1- \cos\left(60\right)^2\right)\tan\left(30\right)$

 Why is 1 - cos(x)^2 = sin(x)^2 ?

 

Solve the product $2\left(1- \cos\left(60\right)^2\right)\tan\left(30\right)$

$\left(2-2\cdot \cos\left(60\right)^2\right)\tan\left(30\right)$

 

Multiply the single term $\tan\left(30\right)$ by each term of the polynomial $\left(2-2\cdot \cos\left(60\right)^2\right)$

$2\tan\left(30\right)-2\cdot \cos\left(60\right)^2\tan\left(30\right)$

 

Cancel like terms $2\tan\left(30\right)$ and $-2\cdot \cos\left(60\right)^2\tan\left(30\right)$

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