Use the trigonometric substitution u = a tan $\theta $, where 0

Question

Use the trigonometric substitution u = a tan $\theta $, where 0 < $\theta $ < $\pi $/2 and to simplify the expression $\sqrt { a ^ { 2 } + u ^ { 2 } }$ . 
A) - a sec $\theta $
B) a sec $\theta $
C) a tan $\theta $
D) a sin $\theta $
E) a csc$\theta $

Quizplus · Accepted Answer

Using the trigonometric substitution $u = a \tan(\theta)$, we can express $\sqrt{a^2 + u^2}$ as $\sqrt{a^2 + (a\tan(\theta))^2}$. Simplifying inside the square root gives $\sqrt{a^2(1 + \tan^2(\theta))}$. Using the trigonometric identity $1 + \tan^2(\theta) = \sec^2(\theta)$, we get $\sqrt{a^2\sec^2(\theta)}$, which simplifies to $a\sec(\theta)$.

Use the Trigonometric Substitution U = a Tan θ\theta θ , Where 0

Use the Trigonometric Substitution U = a Tan $\theta$ , Where 0