Choice 1. He did not square 40, he just multiplied by 2.
Step-by-step explanation:
Step 1:
According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
The hypotenuse measures c cm while the other sides are 40 cm and 9 cm each.
Step 2:
According to the Pythagorean theorem,
![9^{2} +40^{2} = c^{2}.](https://tex.z-dn.net/?f=9%5E%7B2%7D%20%2B40%5E%7B2%7D%20%3D%20c%5E%7B2%7D.)
![81 + 1600 = c^{2} .](https://tex.z-dn.net/?f=81%20%2B%201600%20%3D%20c%5E%7B2%7D%20.)
![1681 = c^{2} .](https://tex.z-dn.net/?f=1681%20%3D%20c%5E%7B2%7D%20.)
![\sqrt{1681} = c.](https://tex.z-dn.net/?f=%5Csqrt%7B1681%7D%20%3D%20c.)
This is the correct solution to the given problem. Hans did not square 40, he just multiplied by 2. Which is the first option.
The trigonometric identity (cos⁴θ - sin⁴θ)/(1 - tan⁴θ) = cos⁴θ
<h3>
How to solve the trigonometric identity?</h3>
Since (cos⁴θ - sin⁴θ)/(1 - tan⁴θ) = [(cos²θ)² - (sin²θ)²]/[1 - (tan²θ)²]
Using the identity a² - b² = (a + b)(a - b), we have
(cos⁴θ - sin⁴θ)/(1 - tan⁴θ) = [(cos²θ)² - (sin²θ)²]/[1 - (tan²θ)²]
= (cos²θ - sin²θ)(cos²θ + sin²θ)/[(1 - tan²θ)(1 + tan²θ)] =
= (cos²θ - sin²θ) × 1/[(1 - tan²θ)sec²θ] (since (cos²θ + sin²θ) = 1 and 1 + tan²θ = sec²θ)
Also, Using the identity a² - b² = (a + b)(a - b), we have
(cos²θ - sin²θ) × 1/[(1 - tan²θ)sec²θ] = (cosθ - sinθ)(cosθ + sinθ)/[(1 - tanθ)(1 + tanθ)sec²θ]
= (cosθ - sinθ)(cosθ + sinθ)/[(cosθ - sinθ)/cosθ × (cosθ + sinθ)/cosθ × sec²θ]
= (cosθ - sinθ)(cosθ + sinθ)/[(cosθ - sinθ)(cosθ + sinθ)/cos²θ × 1/cos²θ]
= (cosθ - sinθ)(cosθ + sinθ)cos⁴θ/[(cosθ - sinθ)(cosθ + sinθ)]
= 1 × cos⁴θ
= cos⁴θ
So, the trigonometric identity (cos⁴θ - sin⁴θ)/(1 - tan⁴θ) = cos⁴θ
Learn more about trigonometric identities here:
brainly.com/question/27990864
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Answer:
12
Step-by-step explanation:
1,2,3,4,6 and 12 all go into the number 12