Question

Sec(tan^-1 x) ka interigation

Answer 1

Explanation:

To Simplify: sec(tan-1x)

Let, 

y = tan-1x

⇒ x = tan y

⇒ x = sin y / cos y            (Since, tan y = sin y / cos y)

Squaring on both the sides,

⇒ x2 = sin2y / cos2y

Adding 1 on both the sides of the equation,

⇒ x2 + 1 = (sin2y / cos2y) + 1

⇒ x2 + 1 = (sin2y + cos2y) / cos2y

⇒ x2 + 1 = 1 / cos2y               (Since, sin2y + cos2y = 1)

⇒ x2 + 1 = sec2y

Taking square root on both the sides,

⇒ √x2 + 1 = sec2y

⇒ √x2 + 1 = sec(tan-1x)           (Since, y = tan-1x)

Thus, the value of sec(tan-1x) is √x2 + 1.