Question

If y=sec x show that, y_(2)=y(2y^2-1)

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Step-by-step explanation:

Given that y = secx

Have to prove that y"= y(2y²–1)

Left hand side,

y = secx

y' = secx.tanx

y" = tanx. secx.tanx + sec².secx

= tan²x.secx + sec³x

= secx ( tan²x+ sec²x)

= secx (2 tan²x +1) [sec²x=tan²+1]

Now,

Right hand side,

y(2y²–1)

=secx( 2sec²x–1)

=secx {2 ( 1 + tan²x) – 1 }

= secx ( 2 tan²x +1)

LHS = RHS

if y = secx then y"= y(2y²–1) (proved)