CBSE Class 12-science Answered

Let secx + tanx = t .............. [1]

thus, { secx - tanx } = 1 / t .....[2]

solving , 1 & , 2 , we get,

secx = t² + 1 / 2t .....[3]

Now , again consider secx + tanx = t

Differentiating both sides , with respect to 'x ' , we get,

secx* tanx + sec² x = dt / dx

secx { secx + tanx } = dt / dx

secx { t } = dt/ dx ... ..[4]

putting the value of secx from [3] in [4], we get,

dx = dt * 2 / [ t² + 1 ]

Now, put the value of t to get the answer.