Question

Prove that sec is an increasing function in(0,π/2).

Answer 1

Dear Student:

We know plot of sinx

So,using sinx we will find nature of secx in (0.π/2)

We will find slope of secx and will observe in (0.π/2)

See the attachment.

Answer 2

concept :- we know, any function , f(x) is increasing in (a, b) only when f'(x) > 0 in interval (a,b ) .

we have to prove that secx is an increasing function in (0, π/2)

Let f(x) = secx

now, differentiate with respect to x,

f'(x) = secx.tanx

now, in 0 < x < π/2 , secx > 0
also in 0 < x < π/2 , tanx > 0
so, f'(x) = secx.tanx > 0 or, f'(x) > 0

since, f'(x) > 0 in (0, π/2) so, function , f(x) = secx is increasing in interval (0, π/2)