QuestionMarch 3, 2026

Simplify without a calculator: cos(48^circ )cos(12^circ )-sin(48^circ )sin(12^circ ) =?vee (square ^circ ) =square

Simplify without a calculator: cos(48^circ )cos(12^circ )-sin(48^circ )sin(12^circ ) =?vee (square ^circ ) =square
Simplify without a calculator: cos(48^circ )cos(12^circ )-sin(48^circ )sin(12^circ ) =?vee (square ^circ ) =square

Solution
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Answer

\cos(60^\circ) = \frac{1}{2} Explanation 1. Recognize the trigonometric identity The expression matches the identity **\cos(A)\cos(B) - \sin(A)\sin(B) = \cos(A + B)**. 2. Simplify using the formula Here, A = 48^\circ and B = 12^\circ, so: \cos(48^\circ)\cos(12^\circ) - \sin(48^\circ)\sin(12^\circ) = \cos(48^\circ + 12^\circ) = \cos(60^\circ). 3. Evaluate \cos(60^\circ) \cos(60^\circ) = \frac{1}{2}.

Explanation

1. Recognize the trigonometric identity <br /> The expression matches the identity **$\cos(A)\cos(B) - \sin(A)\sin(B) = \cos(A + B)$**.<br /><br />2. Simplify using the formula <br /> Here, $A = 48^\circ$ and $B = 12^\circ$, so: <br />$\cos(48^\circ)\cos(12^\circ) - \sin(48^\circ)\sin(12^\circ) = \cos(48^\circ + 12^\circ) = \cos(60^\circ)$.<br /><br />3. Evaluate $\cos(60^\circ)$ <br /> $\cos(60^\circ) = \frac{1}{2}$.
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