Simplify the trigonometric expression cos(x)/(1+sin(x))+1sin(x)

 Exercise

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

 

Combine all terms into a single fraction with $1+\sin\left(x\right)$ as common denominator

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

 

When multiplying two powers that have the same base ($1+\sin\left(x\right)$), you can add the exponents

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

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

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