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Apply the formula: $\left(a+b\right)\left(a+c\right)$$=a^2-b^2$, where $a=\sin\left(x\right)$, $b=\cos\left(x\right)$, $c=-\cos\left(x\right)$, $a+c=\sin\left(x\right)+\cos\left(x\right)$ and $a+b=\sin\left(x\right)-\cos\left(x\right)$
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$f\left(x\right)=\sin\left(x\right)^2-\cos\left(x\right)^2+2\cos\left(x\right)^2$
Learn how to solve problems step by step online. f(x)=(sin(x)-cos(x))(sin(x)+cos(x))+2cos(x)^2. Apply the formula: \left(a+b\right)\left(a+c\right)=a^2-b^2, where a=\sin\left(x\right), b=\cos\left(x\right), c=-\cos\left(x\right), a+c=\sin\left(x\right)+\cos\left(x\right) and a+b=\sin\left(x\right)-\cos\left(x\right). Combining like terms -\cos\left(x\right)^2 and 2\cos\left(x\right)^2. Apply the formula: \sin\left(\theta \right)^2+\cos\left(\theta \right)^2=1.
