2 arcsin(x) = arcsin{2x√(1− x^2)

Kita akan belajar bagaimana membuktikan sifat invers fungsi trigonometri  $2arcsin(x)=arcsin(2x\sqrt{1-x^2})$ atau, $2sin^{-1}(x)=sin^{-1}(2x\sqrt{1-x^2})$

Bukti:

Misal, sin⁻¹ x = α

Jadi, sin α = x

Sekarang, sin 2α = 2 sin αcosα $sin2\alpha =2sin\alpha \sqrt{1-sin^2\alpha }$ 

 $sin2\alpha =2x\sqrt{1-x^2}$ 

Jadi,$2\alpha =sin^{-1}\left (2x\sqrt{1-x^2} \right )$   

$2sin^{-1}x=sin^{-1}\left (2x\sqrt{1-x^2} \right )$ 

atau,  

 $2arcsinx=2arcsin\left (2x\sqrt{1-x^2} \right )$ 

Invers Fungsi Trigonometri

• Nilai Umum dan Pokok sin⁻¹ x
• Nilai Umum dan Pokok dari cos⁻¹ x
• Nilai Umum dan Pokok dari tan⁻¹ x
• Nilai Umum dan Pokok dari csc⁻¹ x
• Nilai Umum dan Pokok dari sec⁻¹ x
• Nilai Umum dan Pokok dari cot⁻¹ x
• Nilai Pokok Invers Fungsi Trigonometri  
• Nilai Umum Invers Fungsi Trigonometri  
• arcsin(x) + arccos(x) = 𝜋/2
• arctan(x) + arccot(x) = 𝜋/2
• $tan^{-1}x+tan^{-1}y=tan^{-1}\left ( \frac{x+y}{1-xy} \right )$
• $tan^{-1}x-tan^{-1}y=tan^{-1}\left ( \frac{x-y}{1+xy} \right )$
• $tan^{-1}x+tan^{-1}y+tan^{-1}z=tan^{-1}\left ( \frac{x+y+z-xyz}{1-xy-yz-xz} \right )$
• $cot^{-1}x+cot^{-1}y=cot^{-1}\left (\frac{xy-1}{y+x} \right )$
• $cot^{-1}x-cot^{-1}y=cot^{-1}\left (\frac{xy+1}{y-x} \right )$
• $sin^{-1}x+sin^{-1}y=sin^{-1}(x\sqrt{1-y^2}+y\sqrt{1-x^2})$
• $sin^{-1}x-sin^{-1}y=sin^{-1}(x\sqrt{1-y^2}-y\sqrt{1-x^2})$
• $cos^{-1}x+cos^{-1}y=cos^{-1}(xy-\sqrt{1-x^2} \sqrt{1-y^2})$
• $cos^{-1}x-cos^{-1}y=cos^{-1}(xy+\sqrt{1-x^2} \sqrt{1-y^2})$
• $2sin^{-1}x=sin^{-1}(2x\sqrt{1-x^2})$
• $2cos^{-1}x=cos^{-1}(2x^2-1)$
• $2tan^{-1}x=tan^{-1}\left ( \frac{2x}{1-x^2} \right )=sin^{-1}\left ( \frac{2x}{1+x^2} \right )=cos^{-1}\left ( \frac{1-x^2}{1+x^2} \right )$
• $3sin^{-1}x=sin^{-1}(3x-4x^3)$
• $3cos^{-1}x=cos^{-1}(4x^3-3x)$
• $3tan^{-1}x=tan^{-1}\left ( \frac{3x-x^3}{1-3x^2} \right )$
• Kumpulan Rumus Invers Fungsi Trigonometri  
• Nilai Utama Invers Fungsi Trigonometri
• Soal-soal & Pembahasan Invers Fungsi Trigonometri  

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