6x=sec theta,6/x=tan theta.find 9(x^2-1/x^2)
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Question :-
→ If 6x = sec ∅ and 6/x = tan ∅ , Find the value of 9( x² - 1/x² ) .
Answer :-
→ 1/4 .
Step-by-step explanation :-
We have :
→ 6x = sec ∅ ....... (1) .
And,
→ 6/x = tan∅ ........ (2) .
Adding equation (1) and (2), we get
→ 6x + 6/x = sec ∅ + tan ∅ .
→ 6( x + 1/x ) = ( sec ∅ + tan ∅ ) ......(3).
Substracting equation (2) from (1), we get
→ 6x - 6/x = sec ∅ - tan ∅ .
→ 6( x - 1/x ) = ( sec ∅ - tan ∅ ) .......(4).
Multiplying the corresponding sides of (3) and (4), we get
→ 36( x² - 1/x² ) = ( sec²∅ - tan²∅ ) .
→ 9 × 4( x² - 1/x² ) = ( sec²∅ - tan²∅ ) .
→ 9( x² - 1/x² ) = 1/4 .
[ °•° sec²∅ - tan²∅ = 1 ] .
Hence, 9( x² - 1/x² ) = 1/4 .
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