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The most general solutions of the equati...

The most general solutions of the equation `secx - 1 = (sqrt2 -1) tan x` are given by-

A

`npi+(pi)/(8)`

B

`2npi,2npi+(pi)/(4)`

C

`2npi`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
`1-cosx=(sqrt(2)-1)sinx`
`rArr"sin"(x)/(2){"sin"(x)/(2)-(sqrt(2)-1)"cos"(x)/(2)}=0`
`therefore"sin"(x)/(2)=0`
or `"tan"(x)/(2)=sqrt(2)-1="tan"(45^(@))/(2)`
`rArr(x)/(2)=npior(x)/(2)=npi+(pi)/(8)`
`thereforex=2npi,2npi+(pi)/(4)`
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