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\sin\left(a+b\right)= | [Sum identity]
\sin a\cos b+\cos a\sin b
\cos\left(a+b\right)= | [Sum identity]
\cos a\cos b-\sin a\sin b
\tan\left(a+b\right)= | [Sum identity]
\frac{\tan a+\tan b}{1-\tan a\tan b}
\sin\left(a-b\right)= | [Difference identity]
\sin a\cos b-\cos a\sin b
\cos\left(a-b\right)= | [Difference identity]
\cos a\cos b+\sin a\sin b
\tan\left(a-b\right)= | [Difference identity]
\frac{\tan a-\tan b}{1+\tan a\tan b}
\sin^2\theta+\cos^2\theta= | [Pythagorean identity]
1
\tan^2\theta+1= | [Pythagorean identity]
\sec^2\theta
1+\cot^2\theta= | [Pythagorean identity]
\csc^2\theta