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tan (Bgsin x) =
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A. \(\boldsymbol x \) |
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| B. \(\boldsymbol{x.\sqrt {1-x^2} }\) |
| C. \(\boldsymbol{\sqrt {1-x^2} }\) |
| D. \(\large\boldsymbol{\frac {1} {\sqrt {1-x^2}} }\) |
| E. \(\large\boldsymbol{\frac {x} {\sqrt {1\,-\,x^2}} }\) |
[ 5-1977 - op net sinds 20.3.15-(E)-4.11.2023 ]
Translation in E N G L I S H
IN CONSTRUCTION
tan( arctan(x) ) =
| A. |
|---|
| B. |
| C. |
| D. |
| E. |
Oplossing - Solution
Stel Bgsin x = t. Dan is x = sin t ∧ t ∈ [\(-\,\frac{\pi}{2},+\frac{\pi}{2}\)] (*)
Dus is 1 − x² = 1 − sin² t = cos² t en wegens de formule \(1\!+\!\tan^2\alpha=\frac{1}{\cos^2\alpha}\)
is ook \(\sqrt{1-x^2}=\cos t \) (en NIET − cos t wegens (*) )
Bijgevolg is tan (Bgsin x) = tan t = \(\frac {\sin t} {\cos t}=\frac{x}{\sqrt{1-x^2}} \)
