A) -1/4
B) 1/2
C) 0
D) 3/4
Correct Answer: D
Solution :
\[{{\cos }^{2}}{{76}^{o}}+{{\cos }^{2}}{{16}^{o}}-\cos {{76}^{o}}\cos {{16}^{o}}\] \[=\frac{1}{2}\left[ 1+\cos {{152}^{o}}+1+\cos {{32}^{o}}-\cos {{92}^{o}}-\cos {{60}^{o}} \right]\] \[=\frac{1}{2}\left[ 2-\frac{1}{2}+\cos {{152}^{o}}+\cos {{32}^{o}}-\cos {{92}^{o}} \right]\] \[=\frac{1}{2}\left[ \frac{3}{2}+2\cos {{92}^{o}}\cos {{60}^{o}}-\cos {{92}^{o}} \right]\] \[=\frac{1}{2}\left[ \frac{3}{2}+\cos {{92}^{o}}-\cos {{92}^{o}} \right]\]\[=\frac{3}{4}\].
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