Question

6x=sec theta,6/x=tan theta.find 9(x^2-1/x^2)

Answer 1

I hope it will help you

Answer 2

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 .