Final answer to the problem
$\frac{1-\sin\left(x\right)}{\cos\left(x\right)}$
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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)
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
- Integrate by parts
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1
Applying the tangent identity: $\displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}$
$\sec\left(x\right)+\frac{-\sin\left(x\right)}{\cos\left(x\right)}$
Why is tan(x) = sin(x)/cos(x) ?
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$\sec\left(x\right)+\frac{-\sin\left(x\right)}{\cos\left(x\right)}$
Learn how to solve problems step by step online. Simplify the trigonometric expression sec(x)-tan(x). Applying the tangent identity: \displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}. Applying the secant identity: \displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}. Combine fractions with common denominator \cos\left(x\right).
Final answer to the problem
$\frac{1-\sin\left(x\right)}{\cos\left(x\right)}$
