Question

if 6x=sectheta and 6/x=tantheta.
Find the value of 9(x²-1²/x²)​

Answer 1

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).

Subtracting 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