Maths - Trigonometry Identities

How could you rewrite the hypotenuse in terms of $\cos$ and $\sin$?

\[\frac{\sin \theta}{\cos \theta}\]

In a circle with width $\sin$ and height $\cos$, what could you write because of Pythagorus?

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

How could you simplify $7(1 - \cos^2\theta)$?

\[7\sin^2\theta\]

How could you rewrite $(\cos^4\theta - \sin^4\theta)$ as the difference of two squares?

\[(\cos^2\theta - \sin^2\theta)(\cos^2\theta + \sin^2\theta)\]

How could you simplify $(\cos^2\theta - \sin^2\theta)(\cos^2\theta + \sin^2\theta)$?

\[(\cos^2\theta - \sin^2\theta)\]

How could you rewrite $3\sin\theta - 2\cos\theta = 0$?

\[\tan\theta = \frac{2}{3}\]

What is the formula for $\sin(A \pm B)$?

\[\sin A\cos B \pm \cos A\sin B\]

What is the formula for $\cos(A \pm B)$?

\[\cos A\cos B \mp \sin A\sin B\]

What is the formula for $\tan(A \pm B)$?

\[\frac{\tan A \pm \tan B}{1 \mp \tan A\tan B}\]

What is the formula for $\sin2A$?

\[2\sin A\cos A\]

What is the formula for $\cos2A$?

\[2\cos^2 A - 1\]

What is the formula for $\tan2A$?

\[\frac{2\tan A}{1-\tan^2 A}\]

What are the three formulas for $\cos 2\theta$?

\[\cos^2 \theta - \sin^2 \theta\] \[2\cos^2 \theta - 1\] \[1-2\sin^2 \theta\]

\[\sin(P) + \sin(Q) = 2\sin\left(\frac{P + Q}{2}\right)\cos\left(\frac{P - Q}{2}\right)\]

How can you go about proving this?

Start by considering

\[\sin(A + B) + \sin(A - B)\]

and then make a substitution.