Prove the trigonometric identity cot(b)^2+csc(b)^2=2csc(b)^2-1

 Exercise

$\cot^2b+\csc^2b=2\csc^2b-1$

 

Starting from the left-hand side (LHS) of the identity

$\cot\left(b\right)^2+\csc\left(b\right)^2$

 

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

$\csc\left(b\right)^2-1+\csc\left(b\right)^2$

 

Combining like terms $\csc\left(b\right)^2$ and $\csc\left(b\right)^2$

$2\csc\left(b\right)^2-1$

 

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

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