Use the suggested substitution to write the expression as a trigonometric expression. Simplify your answer as much as possible. Assume 0≤θ≤π2. 9x2+36⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√, x2=cot(θ)

Answer 1

To simplify the expression square root of (9x^2 + 36) with the substitution x^2 = cot (theta) proceed as follows:

Step 1: Substitute x^2

Given the susstitution x^2 = cot (theta), we can express 9x^2 + 36 in terms of (theta):

9x^2 + 36 = 9(cot (theta) ) +36

Step 2: Simplify the expression

Now substitute x^2 into the expression:

9 cot (theta) + 36

Now we can factor out a 9:

= 9 (cot (theta) + 4 )

Step 3: Take the square root

Next, we compute the square root of he expression:

square root of (9(cot (theta) +4) = 3 square root of (cot (theta) + 4)

Step 4: The final computation

Thus, the expression square root of 9x^2 + 36 simplified using the substitution x^2 = cot (theta) is: 3 square root of (cot (theta) + 4)

Solution:

The final simplified expression for square root of (9x2+36)

 with the substitution x^2 = cot⁡ (θ) is 3 square root of ( cot⁡ (θ) + 4).

Final Answer:

3 square root of ( cot⁡ (θ) + 4)

I hope the mathematical calculations (step by step approach) was helpful. Please let me know if you require any more assistance. If anyone in my neighborhood is interested in setting up an in-person math tutoring session. I look forward to hearing from them. Have an amazing day. Doris H.