Trig

Here’s a structured way to create effective flashcards for memorizing these identities:

Front: \sin^2 x + \cos^2 x = ?

Back: 1

Front: \tan^2 x + 1 = ?

Back: \sec^2 x

Front: 1 + \cot^2 x = ?

Back: \csc^2 x

Front: \sin x = ?

Back: \frac{1}{\csc x}

Front: \cos x = ?

Back: \frac{1}{\sec x}

Front: \tan x = ?

Back: \frac{1}{\cot x}

Front: \cot x = ?

Back: \frac{1}{\tan x}

Front: \sin 2x = ?

Back: 2\sin x \cos x

Front: \cos 2x = ?

Back: Multiple forms:

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

2. 2\cos^2 x - 1

3. 1 - 2\sin^2 x

Front: \tan 2x = ?

Back: \frac{2\tan x}{1 - \tan^2 x}

Front: \sin \frac{x}{2} = ?

Back: \pm \sqrt{\frac{1 - \cos x}{2}}

Front: \cos \frac{x}{2} = ?

Back: \pm \sqrt{\frac{1 + \cos x}{2}}

Front: \tan \frac{x}{2} = ?

Back: Multiple forms:

1. \frac{\sin x}{1 + \cos x}

2. \frac{1 - \cos x}{\sin x}

Front: \sin(x \pm y) = ?

Back: \sin x \cos y \pm \cos x \sin y

Front: \cos(x \pm y) = ?

Back: \cos x \cos y \mp \sin x \sin y

Front: \tan(x \pm y) = ?

Back: \frac{\tan x \pm \tan y}{1 \mp \tan x \tan y}