Trigonometric Identities

\sin^2\left(x\right)

1-\cos^2\left(x\right)

\cos^2\left(x\right)

1-\sin^2\left(x\right)

\sin^2\left(x\right)+\cos^2\left(x\right)

1

\csc^2\left(x\right)

1+\cot^2\left(x_{}\right)

\cot^2\left(x_{}\right)

\csc^2\left(x\right)-1

\sec^2\left(x\right)

1+\tan^2\left(x\right)

\tan^2\left(x_{}\right)

\sec^2\left(x\right)-1

\sin\left(x\right)\cos\left(y\right)

\frac12\left(\sin\left(x-y\right)+\sin\left(x+y_{}\right)\right)

\sin\left(x\right)\sin\left(y\right)

\frac12\left(\cos\left(x-y\right)-\cos\left(x+y_{}\right)\right)

\cos\left(x\right)\cos\left(y\right)

\frac12\left(\cos\left(x-y\right)+\cos\left(x+y\right)\right)

\sin\left(2x\right)

2\sin\left(x\right)\cos\left(x\right)

\cos\left(2x\right)

\cos^2\left(x\right)-\sin^2\left(x\right)

\tan\left(2x\right)

\frac{2\tan\left(x\right)}{1-\tan^2\left(x\right)}

\sin^2\left(x_{}\right)

\frac{1-\cos\left(2x\right)}{2}

\cos^2\left(x\right)

\frac{1+\cos\left(2x\right)}{2}

\tan^2\left(x\right)

\frac{1-\cos\left(2x\right)}{1+\cos\left(2x\right)}

a^2-x^2

x=a\sin\left(\theta\right)

x^2-a^2

x=a\sec\left(\theta\right)

a^2+x^2

x=a\tan\left(\theta\right)