Question

sin(tan^-1 x) is equal to​

Answer 1

Answer:

x/√1+x^2

Step-by-step explanation:

let a = tan inverse x

tan a = x

we convert tan invers to sin inverse

we need to find sin a.

For this first we calculate sec a and cos a

We know that

sec square a = 1 + tan square a

sec a = √ 1 + tan square a

sec a = √ 1+x^2

1/cos a = √1 + x^2

1/√1+x^2 = cos a

cos a = 1/√1+x^2

We know that

sin^2 a = 1 - cos^2 a

sin a = √1-cos^2 a

sin a = square root of 1 - (1/√1 + x^2)^2

sin a = √1 - 1/1+ x^2

sin a = √1 + x^2 -1/1-x^2

= x/√1+x^2

sin a = x/√1+x^2

a=sin inverse of x by root 1+x^2

Now solving

sin(tan inverse x)

= sin(a)

= sin(sin inverse (x by root of 1 + x square))

=x/√1+x^2

Hence proved