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h(x) is increasing for x in...

h(x) is increasing for `x in `

A

`(-(pi)/(4),(pi)/(4))`

B

`(-(pi)/(2),-(pi)/(4))uu(pi)/(4),(pi)/(2))`

C

`(-(pi)/(4),0)uu(pi)/(4),(pi)/(2))`

D

`(-(pi)/(2),-(pi)/(4))uu(0,(pi)/(4))`

Text Solution

Verified by Experts

The correct Answer is:
B
h(x) is increasing `rArr h'(x)gt0`
Case I
`{:("(i) "sin 2x gt0 rArr x in (0,(pi)/(2))),("(ii) "f'(sin^(2)x)gtf'(cos^(2)x) rArr tan^(2)x gt1):}}rArr x in ((pi)/(4),(pi)/(2))`
Case II
`{:(" (i)" sin2xlt0 rArr x in (-(pi)/(2)","0)),(" (ii)"f'(sin^(2)x)gtf'(cos^(2)x) rArr tan^(2)xgt1):}}rArr x in ((-pi)/(2),-(pi)/(4))`
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