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Combine all terms into a single fraction with $2\left(1+\cos\left(x\right)\right)$ as common denominator
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$\frac{\left(1-\sin\left(x\right)+\cos\left(x\right)\right)^2+2\sin\left(x\right)\left(1+\cos\left(x\right)\right)}{2\left(1+\cos\left(x\right)\right)}$
Learn how to solve simplify trigonometric expressions problems step by step online. Simplify the trigonometric expression ((1-sin(x)cos(x))^2)/(2(1+cos(x)))+sin(x). Combine all terms into a single fraction with 2\left(1+\cos\left(x\right)\right) as common denominator. Multiply the single term 2 by each term of the polynomial \left(1+\cos\left(x\right)\right). Multiplying polynomials \sin\left(x\right) and 1+\cos\left(x\right). Multiply the single term 2 by each term of the polynomial \left(\sin\left(x\right)+\sin\left(x\right)\cos\left(x\right)\right).