Q.Find the value of $\cos15^\circ$ using the compound angle formula.

As with $75^\circ$, $15^\circ$ can be written as the difference of two standard angles and expanded with the cosine compound-angle formula.

Step 1 — split $15^\circ$ into standard angles. $15^\circ=45^\circ-30^\circ$.

Step 2 — apply the compound-angle formula. $\cos(A-B)=\cos A\cos B+\sin A\sin B$ with $A=45^\circ, B=30^\circ$:

Step 3 — substitute standard values. $=\dfrac{\sqrt2}{2}\cdot\dfrac{\sqrt3}{2}+\dfrac{\sqrt2}{2}\cdot\dfrac12=\dfrac{\sqrt6}{4}+\dfrac{\sqrt2}{4}=\dfrac{\sqrt6+\sqrt2}{4}$. …

Alternatively, split $15^\circ=60^\circ-45^\circ$ and apply the same formula with $A=60^\circ, B=45^\circ$ — a different pair of standard angles th …

Using the wrong sign in $\cos(A-B)=\cos A\cos B+\sin A\sin B$ (some students wrongly keep a minus sign here, confusing it with the $\cos(A+B)$ formula) — remember the sig …