Question

If 5x = sec θ and $\frac{5}{x} =tan\Theta$, find the value of $5(x^{2} -\frac{1}{x^{2}})$.

Answer 1

Answer:

The value of 5(x² - 1/x²) is ⅕ .

Step-by-step explanation:

Given : 5x = secθ & 5/x = tanθ

By using  an identity, (sec²θ -  tan²θ) = 1

(sec²θ -  tan²θ) = 1

(5x)² - (5/x)² = 1

25x² - 25/x² = 1

25(x² - 1/x²) = 1

(x² - 1/x²) = 1/25 ………(1)

 

We have to find the value of 5(x² - 1/x²) :  

5(x² - 1/x²) = 5(1/25)

[From eq 1]

5(x² - 1/x²) = ⅕  

Hence, the value of 5(x² - 1/x²) is ⅕ .

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Answer 2

(αttαchєd fígurє)

➟ 5(x² - 1/x²) = 1/5

Kindly refer to the attachment, the attachment contains step by step explanation with answer.

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