Simplify the trigonometric expression sin(x)^2-cos(x)sec(x)

 Exercise

$\sin^2\left(x\right)-\cos\left(x\right)\sec\left(x\right)$

 

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

$\sin\left(x\right)^2+\cos\left(x\right)\frac{-1}{\cos\left(x\right)}$

 

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

$\sin\left(x\right)^2+\frac{-\cos\left(x\right)}{\cos\left(x\right)}$

 

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

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

 

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

$-\cos\left(x\right)^2$

$-\cos\left(x\right)^2$

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