Final answer to the problem
$\frac{\left(\sin\left(x\right)+1\right)^{2}}{1+\sin\left(x\right)\left(1+\cos\left(x\right)\right)+\cos\left(x\right)}$
Step-by-step Solution
Learn how to solve simplify trigonometric expressions problems step by step online. \frac{\left(1+ sen x + cos x\right)^2}{\left(tg x + senx\right)\left(cotg x +cos x\right)}. Math interpretation of the question. Expand the expression \left(1+\sin\left(x\right)+\cos\left(x\right)\right)^2 using the square of a binomial: (a+b)^2=a^2+2ab+b^2. Multiply the single term \cot\left(x\right)+\cos\left(x\right) by each term of the polynomial \left(\tan\left(x\right)+\sin\left(x\right)\right). Multiply the single term \tan\left(x\right) by each term of the polynomial \left(\cot\left(x\right)+\cos\left(x\right)\right).
Final answer to the problem
$\frac{\left(\sin\left(x\right)+1\right)^{2}}{1+\sin\left(x\right)\left(1+\cos\left(x\right)\right)+\cos\left(x\right)}$
