sin(tan^−1x), |x|<1 is equal to x/sqrt(1+x^2) 1/sqrt(1+x^2) x/sqrt(1−x^2)

mazilievdbf

mazilievdbf

Answered question

2023-02-17

sin(tan^−1x), |x|<1 is equal to
x/sqrt(1+x^2)
1/sqrt(1+x^2)
x/sqrt(1−x^2)

Answer & Explanation

Karli Foley

Karli Foley

Beginner2023-02-18Added 4 answers

θ = tan 1 x , x = tan θ sin ( tan 1 x ) = sin θ sin ( tan 1 x ) = 1 c o s e c θ = 1 1 + c o t 2 θ sin ( tan 1 x ) = 1 1 + c o t 2 θ sin ( tan 1 x ) = 1 1 + 1 tan 2 θ sin ( tan 1 x ) = 1 1 + 1 ( tan ( tan 1 x ) ) 2 sin ( tan 1 x ) = 1 1 + 1 x 2 = x x 2 + 1

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