Simplify the trigonometric expression cos(x)(tan(x)-sec(x))-sin(x)+-1

 Exercise

$cosx\left(tanx-secx\right)-sinx-1$

 

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

$\tan\left(x\right)\cos\left(x\right)-\sec\left(x\right)\cos\left(x\right)-\sin\left(x\right)-1$

 

Applying the secant identity: $\displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}$

$\tan\left(x\right)\cos\left(x\right)+\frac{-1}{\cos\left(x\right)}\cos\left(x\right)-\sin\left(x\right)-1$

 

Multiplying the fraction by $\cos\left(x\right)$

$\tan\left(x\right)\cos\left(x\right)+\frac{-\cos\left(x\right)}{\cos\left(x\right)}-\sin\left(x\right)-1$

 

Simplify the fraction $\frac{-\cos\left(x\right)}{\cos\left(x\right)}$ by $\cos\left(x\right)$

$\tan\left(x\right)\cos\left(x\right)-1-\sin\left(x\right)-1$

 

Subtract the values $-1$ and $-1$

$\tan\left(x\right)\cos\left(x\right)-2-\sin\left(x\right)$

$\tan\left(x\right)\cos\left(x\right)-2-\sin\left(x\right)$

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