(6cos 24-6sin 24)tan48

(6cos²24°-6sin²24°)tan48°

\(\begin{array}{|rcll|} \hline &&\mathbf{ (6\cos^224^\circ-6\sin^224^\circ)\tan48^\circ } \\\\ &=& 6\cdot (\cos^224^\circ-\sin^224^\circ)\tan(48^\circ) \quad | \quad \cos(48^\circ) = \cos^2(24^\circ) - \sin^2(24^\circ) \\\\ &=& 6\cdot \cos(48^\circ)\cdot \tan(48^\circ) \quad | \quad \tan(48^\circ) = \dfrac{\sin(48^\circ)}{\cos(48^\circ)} \\\\ &=& 6\cdot \cos(48^\circ)\cdot \dfrac{\sin(48^\circ)}{\cos(48^\circ)} \\\\ &=& 6\cdot \dfrac{\sin(48^\circ)\cos(48^\circ)}{\cos(48^\circ)} \\\\ &\mathbf{=}& \mathbf{6\cdot \sin(48^\circ)} \\ \hline \end{array} \)

\((6cos^2 24°-6sin^2 24°)tan48°\)

I used the double angle identity \(cos2A = cos^2 A-sin^2 A \)

and I got \(6cos2(24)°(tan48°)\)

I could change the tan to sin/cos but then I'm not sure what to do next?

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\(6cos[\color{red}{2(24)}\color{black}{]°(tan48°)}\\ =6cos[\color{red}{48}\color{black}{]°(tan48°)}\\ =6cos[\color{red}{48}\color{black}{]°\cdot\frac{sin48}{cos48}}\\ =6sin48\)