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cluponka [151]
4 years ago
15

Simplify tan9x-tan5x / 1+tan9xtan5x (SHOW WORK)

Mathematics
1 answer:
Charra [1.4K]4 years ago
4 0

Answer:

The simplest form is tan(4x)

Step-by-step explanation:

* Lets revise the identity of the compound angles

- tan(a+b)=\frac{tan(a)+tan(b)}{1-tan(a)tan(b)}

- tan(a-b)=\frac{tan(a)-tan(b)}{1+tan(a)tan(b)}

* Lets solve the problem

- Let 9x = 5x + 4x

∴ tan(9x) = tan(5x + 4x)

- Use the rule of the compound angle

∵ \frac{tan(9x)-tan(5x)}{1+tan(9x)tan(5x)} ⇒ (1)

∵ tan(5x+4x)=\frac{tan(5x)+tan(4x)}{1-tan(5x)tan(4x)} ⇒ (2)

∵ tan(9x) = equation (2)

- Substitute (2) in (1)

∴ \frac{\frac{tan(5x)+tan(4x)}{1-tan(5x)tan(4x)}-tan(5x)}{1+(\frac{tan(5x)+tan(4x)}{1-tan(5x)tan(4x)})tan(5x)}

- Multiply up and down by (1 - tan(5x)tan(4x))

∴ \frac{tan(5x)+tan(4x)-tan(5x)[1-tan(5x)tan(4x)]}{1-tan(5x)tan(4x)+tan(5x)[tan(5x)+tan(4x)]}

- Simplify up and down

∴ \frac{tan(5x)+tan(4x)-tan(5x)+tan^{2}(5x)tan(4x)}{1-tan(5x)tan(4x)+tan^{2}(5x)+tan(5x)tan(4x) }

∴ \frac{tan(4x)+tan^{2}(5x)tan(4x)}{[1+tan^{2}(5x)]}

- Take tan(4x) as a common factor up

∴ \frac{tan(4x)[1+tan^{2}(5x)]}{[1+tan^{2}(5x)]}

- Cancel [1 + tan²(5x)] up and down

∴ The answer is tan(4x)

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

Given that:

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To find:

The equation and solution to represent the difference the original price d of the markers and the coupon.

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A baseball diamond is a square that is 90 feet on each side. What is the distance from home to second base?
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Explanation:

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For instance, if we multiply two numbers that are each in the hundredths place, we will have 2+2 = 4 decimal numbers in our answer. If our answer gives us only 3 digits, we place a zero in front and then place the decimal.

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