Question

If 3x =sec theta and 3/x=tan theta,then find the value of :x^2-1/x

Answer 1

3x = sec∅ => x = secx/3
3/x = tan∅ => 1/x = tanx/3

then, (x² - 1)/x = x²/x - 1/x
= x - 1/x = (secx/3 - tanx/3)
= (secx - tanx)/3

hence, (x² - 1)/x = (sec - tanx)/3

Answer 2

3x = sec∅ => x = secx/3

3/x = tan∅ => 1/x = tanx/3

then, (x² - 1)/x = x²/x - 1/x

= x - 1/x = (secx/3 - tanx/3)

= (secx - tanx)/3

hence, (x² - 1)/x = (sec - tanx)/3