Expand and simplify the trigonometric expression 1/cos(x)(1/cos(x)+sin(x)/cos(x))

 Exercise

$\frac{1}{cosx}\left(\frac{1}{cosx}+\frac{sinx}{cosx}\right)$

 

Combine fractions with common denominator $\cos\left(x\right)$

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

 

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

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

 

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

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

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

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