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amit kumar

· started a discussion

· 1 Months ago

algebra (Question: 196627.0 )

1/16 is right

Question:
If 4x = sec\(\theta\) and \(\cfrac{4}{x}\) = tan\(\theta\), then find the value of 8 \(\left (x^2 - \cfrac {1}{x^2} \right )\)
Options:
A) \(\cfrac{1}{2}\)
B) \(\cfrac{1}{4}\)
C) \(\cfrac{1}{16}\)
D) \(\cfrac{1}{8}\)
Solution:
Ans: (a)

4x = sec\(\theta\)

\(\cfrac{4}{x}\) = tan\(\theta\)

4x + \(\cfrac{4}{x}\) = sec\(\theta\) + tan\(\theta\)..... (i)

4x – \(\cfrac{4}{x}\) = sec\(\theta\) – tan\(\theta\).....(ii)

Multiplying equation (i) and (ii)

\(\left (4x + \cfrac {4}{x} \right ) \ \left (4x - \cfrac {4}{x} \right )\) = (sec\(\theta\) + tan\(\theta\))

(sec\(\theta\) – tan\(\theta\))

16 \(\left (x^2 - \cfrac {1}{x^2} \right )\) = sec2 \(\theta\) – tan2\(\theta\)

8 \(\left (x^2 - \cfrac {1}{x^2} \right )\) =  \(\cfrac{1}{2}\) × 1

[sec2\(\theta\) – tan2\(\theta\) = 1]

8 \(\left (x^2 - \cfrac {1}{x^2} \right )\) =  \(\cfrac{1}{2}\) .

bablu chandora

· commented

· 1 Months ago

explain bro

Subhadip

· commented

· 1 Months ago

1/16
is ryt
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