Question

Make the substitution =5sin to simplify the expression √25−2

Answer 1

5 cos

Explanation:

We have the following expression:

`√(25-x^2)`

We substitute when x = 5 sin and get the following:

`\begin{gathered} √(25-\left(5\sin\left(\theta\right)\right)^2) \\ \\ √(25-5^2\sin^2\left(\theta\right)) \\ \\ 25-5^2\sin^2(\theta)=25\cdot\:1-25\sin^2\left(\theta\right)=25\left(1-\sin^2\left(\theta\right)\right) \\ \\ √(25\left(1-\sin^2\left(\theta\right)\right))=√(25)\cdot√(1-\sin^2\left(\theta\right))=5√(\cos^2\left(\theta\right))=5\cos\theta \\ \end{gathered}`