समीकरण `sec theta - 1 = (sqrt(2)-1)tan theta` को हल कीजिए |

Explanation

`sec theta - 1 = (sqrt(2)-1)tan theta`
`rArr " " (1)/(cos theta)-1=(sqrt(2)-1).(sin theta)/(cos theta)`
`rArr " " 1-cos theta = (sqrt(2)-1)sin theta`
`rArr " 2 sin"^(2)(theta)/(2)=(sqrt(2)-1)."2 sin"(theta)/(2)."cos"(theta)/(2)`
`rArr " sin"^(theta)/(2)["sin"(theta)/(2)-(sqrt(2)-1)"cos"(theta)/(2)=0`
`rArr " sin"(theta)/(2)=0 " "` या `" sin"(theta)/(2)=(sqrt(2)-1)"cos"(theta)/(2)`
`rArr " sin"(theta)/(2)=0 " "` या `" tan" (theta)/(2)=sqrt(2)-1`
`rArr " sin"(theta)/(2)=0=sin 0 " "` या `" tan"(theta)/(2)=sqrt(2)-1="tan"(pi)/(8)`
`rArr " "(theta)/(2)= n pi " "` या `" " (theta)/(2)=n pi + (pi)/(8)`
`rArr " " theta = 2 n pi, n in I " "` या `" " theta = 2n pi +(pi)/(4), n in I`.