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\sin\theta=\frac{opposite}{hypotenuse},\cos\theta=\frac{adjacent}{hypotenuse},\tan\theta=\frac{opposite}{adjacent}

\sin\theta=\frac{1}{\csc\theta},\cos\theta=\frac{1}{\sec\theta},\tan\theta=\frac{\sin\theta}{\cos\theta}=\frac{1}{\cot\theta}

\csc\theta=\frac{1}{\sin\theta},\sec\theta=\frac{1}{\cos\theta},\cot\theta=\frac{\cos\theta}{\sin\theta}=\frac{1}{\tan\theta}

\sin\theta=\cos\left(\frac{\pi}{2}-\theta\right),\cos\theta=\sin\left(\frac{\pi}{2}-\theta\right)

\tan\theta=\cot\left(\frac{\pi}{2}-\theta\right),\cot\theta=\tan\left(\frac{\pi}{2}-\theta\right)

\sin^2\theta+\cos^2\theta=1

(\sin\theta)^2+(\cos\theta)^2=1

\sin(x+y)=\sin x \cos y+\cos x \sin y

\sin(x-y)=\sin x \cos y-\cos x \sin y

\cos(x+y)=\cos x \cos y-\sin x \sin y

\cos(x-y)=\cos x \cos y+\sin x \sin y

\sin 2x=2\sin x \cos x

\cos 2x=\cos^2 x-\sin^2 x=2\cos^2 x-1=1-2\sin^2 x

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