Bentuk identitas trigonometri
[tex]\displaystyle \frac{1+\sin x-\cos x}{1+\sin x+\cos x}+\frac{1+\sin x+\cos x}{1+\sin x-\cos x}[/tex]
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[tex]\displaystyle \frac{1+\sin x-\cos x}{1+\sin x+\cos x}+\frac{1+\sin x+\cos x}{1+\sin x-\cos x}[/tex]
apabila disederhanakan menjadi ...
Verified answer
Materi : Trigonometri
[tex][tex]\displaystyle \frac{1+\sin x-\cos x}{1+\sin x+\cos x}+\frac{1+\sin x+\cos x}{1+\sin x-\cos x}[/tex][/tex]
( 1 + sin x + cos x )/( 1 + sin x - cos x ) + ( 1 + sin x - cos x )/( 1 + sin x + cos x )
Sama kedua pecahan
= [ ( 1 + sin x + cos x )² + ( 1 + sin x - cos x )² ]/[ ( 1 + sin x + cos x )( 1 + sin x - cos x ) ]
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( 1 + sin x + cos x )²
= sin² x + cos² x + 2.sin x.cos x + 2.sin x + 2.cos x + 1
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( 1 + sin x - cos x )²
= sin² x + cos² x - 2.sin x.cos x + 2.sin x - 2.cos x + 1
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( 1 + sin x + cos x )( 1 + sin x - cos x )
= sin² x + cos² x + 2.sin x + 1
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= ( 2[ sin² x + cos² x ] + 4.sin x + 2 )/( sin² x + cos² x + 2.sin x + 1 )
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Dengan rumus sin² x + cos² x = 1
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= ( 2[1] + 4.sin x + 2 )/( [1] + 2.sin x + 1 )
= ( 4.sin x + 4 )/( 2.sin x + 2 )
= 4/2( sin x + 1 )
= 2.sin x + 2
Semoga bisa membantu
[tex] \boxed{ \colorbox{darkblue}{ \sf{ \color{lightblue}{ answered\:by\: BLUEBRAXGEOMETRY}}}} [/tex]