Hola ^○^buktikan bahwa...[tex]\bf \frac{ { cos}^{2} x - { cos}^{4}x }{1 - {sin}^{2} x} + \frac{ {sin.... Question from @nafirahmulya

August 2022 2 21 Report

Hola ^○^

buktikan bahwa...

[tex]\bf \frac{ { cos}^{2} x - { cos}^{4}x }{1 - {sin}^{2} x} + \frac{ {sin}^{2}x - {sin}^{4} x}{1 - {cos}^{2} x} = 1 \\ [/tex]

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ErichelFr

$\sf\dfrac{ { cos}^{2} x - { cos}^{4}x }{1 - {sin}^{2} x} + \dfrac{ {sin}^{2}x - {sin}^{4} x}{1 - {cos}^{2} x} = 1$

$\sf\dfrac{cos^{2}x ({1 - cos}^{2})}{cos^{2}x } + \dfrac{ sin^{2}x(1 - {sin}^{2}x )}{{sin}^{2} x} = 1$

$\sf\dfrac{ \cancel{cos^{2}x }( {1 - cos}^{2})}{ \cancel{cos{^2}x} } + \dfrac{ \cancel{sin^{2}x}(1 - {sin}^{2}x )}{ \cancel{{sin}^{2} x}} = 1$

$\sf ({1 - cos}^{2})+ (1 - {sin}^{2}x ) = 1$

$\sf {sin}^{2}x+ {cos}^{2}x = 1 \: \: \: \: \: \: \: \: \: \to identitas \: trigonometri$

$\sf \: {1 = 1} \: \: \: \: terbukti$

3 votes Thanks 2

misrokhah439 kak Rixxel jawab pertanyaan sy paling atas dong, sepi soalnya gak ada yg jawab, sayang poinnya membazhir :v

ErichelFr ehh males :v

misrokhah439 lah kok males ;-;

ErichelFr okeh kujawab

misrokhah439 hore ＼(^o^)／ ☺️

misrokhah439

$\tt\frac{ { cos}^{2} x - { cos}^{4}x }{1 - {sin}^{2} x} + \frac{ {sin}^{2}x - {sin}^{4} x}{1 - {cos}^{2} x} = 1$

$=\tt\frac{ \cos{x}^{2} - \cos {x}^{4} }{1 - \sin {x}^{2} } + \frac{ \sin {x}^{2} - \sin {x}^{4} }{1 - \cos {x}^{2} }$

$= \tt \frac{(1 - \cos {x}^{2}) \cos {x}^{2} }{ \cos {x}^{2}} + \frac{(1 - \sin {x}^{2}) \times \sin {x}^{2} }{ \sin {x}^{2} }$

$=\tt \sin{x}^{2} + \cos {x}^{2}$

$\bold{=1}$

${\boxed{\tt{terbukti}}}$

1 votes Thanks 2

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