\frac{sec x + tan x }{sec x +1 }

 Exercise

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Math interpretation of the question

$\frac{\sec\left(x\right)+\tan\left(x\right)}{\sec\left(x\right)+1}$

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Rewrite $\frac{\sec\left(x\right)+\tan\left(x\right)}{\sec\left(x\right)+1}$ in terms of sine and cosine functions

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

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

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

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Combine $\frac{1}{\cos\left(x\right)}+1$ in a single fraction

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

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

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

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

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