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Exercise

$\frac{sec\theta\:\:}{1-\sin\:\left(\theta\:\right)}$

Step-by-step Solution

1

Apply the trigonometric identity: $\frac{\sec\left(\theta \right)}{b}$$=\frac{1}{b\cos\left(\theta \right)}$, where $b=1-\sin\left(\theta\right)$ and $x=\theta$

$\frac{1}{\left(1-\sin\left(\theta\right)\right)\cos\left(\theta\right)}$

Final answer to the exercise

$\frac{1}{\left(1-\sin\left(\theta\right)\right)\cos\left(\theta\right)}$

Try other ways to solve this exercise

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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
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$\frac{2+tan^2x}{sec^2x}-1$

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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