Prove the trigonometric identity 2cos(a)^2-1=1-2sin(a)^2

 Exercise

$2\cos^2a-1=1-2\sin^2a$

 

Starting from the right-hand side (RHS) of the identity

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

 

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

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

 Why is 1 - cos(x)^2 = sin(x)^2 ?

 

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

$1-2+2\cos\left(a\right)^2$

 

Add the values $1$ and $-2$

$-1+2\cos\left(a\right)^2$

 

Since we have reached the expression of our goal, we have proven the identity

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