\frac{\left(1+ sen x + cos x\right)^2}{\left(tg x + senx\right)\left(cotg x +cos x\right)}

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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

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  • Find the derivative
  • Integrate using basic integrals
  • Verify if true (using algebra)
  • Verify if true (using arithmetic)
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Math interpretation of the question

Learn how to solve simplify trigonometric expressions problems step by step online.

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

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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

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

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Main Topic: Simplify Trigonometric Expressions

Simplification of trigonometric expressions consists of rewriting an expression with trigonometric functions in a simpler form. To perform this task, we usually use the most common trigonometric identities, and some algebra.

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