Half Angle Form

Geometry Level 5

F i n d sin ⁡ − 1 2 x 1 + x 2 w h e n x > 1 Find\quad \sin ^{ -1 }{ \frac { 2x }{ 1+{ x }^{ 2 } } } \quad when\quad x>1

2 tan ⁡ − 1 x 2\tan ^{ -1 }{ x } π − 2 tan ⁡ − 1 2 x 2 1 − x 2 \pi -2\tan ^{ -1 }{ \frac { 2{ x }^{ 2 } }{ 1-{ x }^{ 2 } } } π − 2 tan ⁡ − 1 x \pi -2\tan ^{ -1 }{ x } none of these

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Samarth Sangam by samarth sangam , 23, India

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1 solution

Samarth Sangam
Oct 14, 2014

s i n c e x > 1 sin ⁡ − 1 2 x 1 + x 2 = π − 2 tan ⁡ − 1 x \ since\quad x>1\quad \\ \sin ^{ -1 }{ \frac { 2x }{ 1+{ x }^{ 2 } } } =\quad \pi -2\tan ^{ -1 }{ x }

2 Helpful 0 Interesting 0 Brilliant 0 Confused

The first line is not true. Take x = 0.5, then you are saying that sin ⁡ − 1 1 0.75 = 2 tan ⁡ − 1 0.5 \sin ^{-1} \frac{1}{0.75} = 2 \tan^{-1} 0.5 . However, the LHS is complex valued, while the RHS is real valued.

Calvin Lin Staff - 6 years, 8 months ago

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