Simplify the trigonometric expression cos(t)(csc(t)-sec(t))+1

 Exercise

$cos\theta\:\left(csc\theta\:-sec\theta\:\right)+1$

 

Multiply the single term $\cos\left(\theta\right)$ by each term of the polynomial $\left(\csc\left(\theta\right)-\sec\left(\theta\right)\right)$

$\csc\left(\theta\right)\cos\left(\theta\right)-\sec\left(\theta\right)\cos\left(\theta\right)+1$

 

Applying the trigonometric identity: $\cos\left(\theta \right)\sec\left(\theta \right) = 1$

$\csc\left(\theta\right)\cos\left(\theta\right)-1+1$

 

Subtract the values $1$ and $-1$

$\csc\left(\theta\right)\cos\left(\theta\right)+0$

 

$x+0=x$, where $x$ is any expression

$\csc\left(\theta\right)\cos\left(\theta\right)$

 

Simplify $\csc\left(\theta\right)\cos\left(\theta\right)$ into $\cot(\theta)$ by applying trigonometric identities

$\cot\left(\theta\right)$

$\cot\left(\theta\right)$

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