Evaluate: cos^2 48^circ - sin^2 12^circ | vedclass

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Question

(B) We use the trigonometric identity: $\cos^2 A - \sin^2 B = \cos(A + B) \cos(A - B)$.Substituting $A = 48^\circ$ and $B = 12^\circ$:$\cos^2 48^\circ

Vedclass · Accepted Answer

$\frac{\sqrt{5} + 1}{8}$

Vedclass · Answer

(B) We use the trigonometric identity: $\cos^2 A - \sin^2 B = \cos(A + B) \cos(A - B)$.Substituting $A = 48^\circ$ and $B = 12^\circ$:$\cos^2 48^\circ - \sin^2 12^\circ = \cos(48^\circ + 12^\circ) \cos(48^\circ - 12^\circ)$$= \cos 60^\circ \cos 36^\circ$We know that $\cos 60^\circ = \frac{1}{2}$ and $\cos 36^\circ = \frac{\sqrt{5} + 1}{4}$.Therefore,the expression becomes:$= \frac{1}{2} 	imes \left( \frac{\sqrt{5} + 1}{4} ight) = \frac{\sqrt{5} + 1}{8}$.

Evaluate: $\cos^2 48^\circ - \sin^2 12^\circ$

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