Make the Trigonometric Substitution $$x = a \tan \theta \text { for } \frac { - \pi } { 2 } < \theta < \frac { \pi } { 2 }$$

question 21

Multiple Choice

Make the trigonometric substitution $$x = a \tan \theta \text { for } \frac { - \pi } { 2 } < \theta < \frac { \pi } { 2 }$$ and a > 0. Use fundamental identities to simplify the resulting expression. $\frac { 1 } { x ^ { 2 } + a ^ { 2 } }$

• A) \(a ^ { 2 } \sec ^ { 2 } \theta \csc \theta\)
• B) \(\frac { 1 } { a } \cos ^ { 2 } \theta\)
• C) \(\frac { 1 } { a } \cos \theta\)
• D) \(\frac { 1 } { a ^ { 2 } } \cos ^ { 2 } \theta\)
• E) \(a \sec \theta\)

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