Question

If 4x=sec theta and 4/x=tan theta,find 8(x^2-1/x^2)

Answer 1

Hi ,

Given

here I am taking A instead of theta ,

4x = sec A --- ( 1 )

4/x= tan A -----( 2 )

we know the trigonometric identity

sec² A - tan² A = 1

( 4x )² - ( 4/x )² = 1 from ( 1 ) and ( 2 ),

16x² - 16 / x² = 1

16( x² - 1/x² ) = 1

2× 8 ( x² - 1 / x² ) = 1

Therefore ,

8( x² - 1 / x² ) = 1/2

I hope this helps you.

:)

Answer 2

Answer:

1/2

Step-by-step explanation:

sec²theta-tan²theta=1

(4x)²-(4/x)²=1

8(x²-1/x²)=1/2