Prove that tan ⁡ ( arcsin ⁡ ( x ) ) = tan ⁡ θ...

pipantasi4

pipantasi4

Answered

2022-07-07

Prove that
tan ( arcsin ( x ) ) = tan θ = x 1 x 2 for 0 x < 1

Answer & Explanation

Sophia Mcdowell

Sophia Mcdowell

Expert

2022-07-08Added 14 answers

The very last step can be translated to
0 x < 1 tan ( arcsin ( x ) ) = tan ( arcsin ( x ) ) = tan ( arcsin ( x ) ) = x 1 x 2 ,
equivalent to
1 < x 0 tan ( arcsin ( x ) ) = x 1 x 2 .
Oddness of the functions allows the minus sign to "cross" them.

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