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\csc^2x
1+\cot^2x=? [Pythagorean]
1
\sin^2x+\cos^2x=? [Pythagorean]
\sec^2x
\tan^2x+1=? [Pythagorean]
\frac12\left(1-\cos2x\right)
\sin^2x=? [Half-Angle]
\frac12\left(1+\cos2x\right)
\cos^2x=? [Half-Angle]
2\sin x\cos x
\sin2x=? [Double-Angle]
\cos^2x-\sin^2x
\cos2x=? [Double-Angle]
\frac{\sin x}{\cos x}
\tan x=? [terms of sine and cosine]