cos2⁡76∘+cos2⁡16∘−cos⁡76∘cos⁡16∘=

=cos2⁡76∘+1−sin2⁡16∘−(1/2)2cos⁡76∘cos⁡16∘=1+cos⁡92∘cos⁡60∘−(1/2)cos⁡92∘+cos⁡60∘=1+cos⁡92∘(1/2)−(1/2)cos⁡92∘−(1/2)(1/2)=1−(1/4)=3/4

cos2⁡76∘+cos2⁡16∘−cos⁡76∘cos⁡16∘=

=cos2⁡76∘+1−sin2⁡16∘−(1/2)2cos⁡76∘cos⁡16∘=1+cos⁡92∘cos⁡60∘−(1/2)cos⁡92∘+cos⁡60∘=1+cos⁡92∘(1/2)−(1/2)cos⁡92∘−(1/2)(1/2)=1−(1/4)=3/4

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$\cos^{2} 76^{\circ} + \cos^{2} 16^{\circ} - \cos 76^{\circ} \cos 16^{\circ} =$

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1/2

-1/4

3/4

answer is D.

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Detailed Solution

$\begin{array}{l} = \cos^{2} 76^{\circ} + 1 - \sin^{2} 16^{\circ} - (1 / 2) [2 \cos 76^{\circ} \cos 16^{\circ}] \\ = 1 + \cos 92^{\circ} \cos 60^{\circ} - (1 / 2) [\cos 92^{\circ} + \cos 60^{\circ}] \\ = 1 + \cos 92^{\circ} (1 / 2) - (1 / 2) \cos 92^{\circ} - (1 / 2) (1 / 2) = 1 - (1 / 4) = 3 / 4 \end{array}$