Rumus Identitas Trigonometri Lengkap

Rumus Identitas Trigonometri

Identitas Dasar

$$\sin^2 x + \cos^2 x = 1$$ $$1 + \tan^2 x = \sec^2 x$$ $$1 + \cot^2 x = \csc^2 x$$

Identitas Perbandingan

$$\tan x = \frac{\sin x}{\cos x}$$ $$\cot x = \frac{\cos x}{\sin x}$$ $$\sec x = \frac{1}{\cos x}$$ $$\csc x = \frac{1}{\sin x}$$

Identitas Resiprok

$$\sin x = \frac{1}{\csc x}$$ $$\cos x = \frac{1}{\sec x}$$ $$\tan x = \frac{1}{\cot x}$$

Jumlah dan Selisih Sudut

$$\sin(A+B)=\sin A\cos B+\cos A\sin B$$ $$\sin(A-B)=\sin A\cos B-\cos A\sin B$$ $$\cos(A+B)=\cos A\cos B-\sin A\sin B$$ $$\cos(A-B)=\cos A\cos B+\sin A\sin B$$ $$\tan(A+B)=\frac{\tan A+\tan B}{1-\tan A\tan B}$$ $$\tan(A-B)=\frac{\tan A-\tan B}{1+\tan A\tan B}$$

Sudut Ganda

$$\sin 2x = 2\sin x \cos x$$ $$\cos 2x = \cos^2 x - \sin^2 x$$ $$\cos 2x = 1 - 2\sin^2 x$$ $$\cos 2x = 2\cos^2 x - 1$$ $$\tan 2x = \frac{2\tan x}{1 - \tan^2 x}$$

Setengah Sudut

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

Perkalian ke Penjumlahan

$$\sin A \sin B = \frac{1}{2}[\cos(A-B) - \cos(A+B)]$$ $$\cos A \cos B = \frac{1}{2}[\cos(A-B) + \cos(A+B)]$$ $$\sin A \cos B = \frac{1}{2}[\sin(A+B) + \sin(A-B)]$$

Penjumlahan ke Perkalian

$$\sin A + \sin B = 2\sin\frac{A+B}{2}\cos\frac{A-B}{2}$$ $$\sin A - \sin B = 2\cos\frac{A+B}{2}\sin\frac{A-B}{2}$$ $$\cos A + \cos B = 2\cos\frac{A+B}{2}\cos\frac{A-B}{2}$$ $$\cos A - \cos B = -2\sin\frac{A+B}{2}\sin\frac{A-B}{2}$$

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