Question

Q.No.11
sin(tan-1 x),|x| <1 is equal to:​

Answer 1

let tan-1 x = y

tan y = x

tan^2 y = x^2

sin^2 y /cos^2 y = x^2

sin^2 y = x^2 cos^2 y

sin^2 y = x^2 (1 - sin^2 y)

sin^2 y = x^2 - x^2 sin^2 y

sin^2 y + x^2 sin^2 y = x^2

sin^2 y (1 + x^2) = x^2

sin^2 y = x^2 / (1 + x^2)

sin y = x / √(1 + x^2)

y = sin-1 (x / √(1 + x^2)

the problem becomes

sin(sin-1 (x / (√1 + x^2)

= x / √1 + x^2

Answer 2

Answer:

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