Tích số cos10°×cos30°×cos50°×cos70° bằng

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Tích số cos10°.cos30°.cos50°.cos70° bằng

\(\frac{1}{{16}}\);

\(\frac{1}{8}\);

\(\frac{3}{{16}}\);

\(\frac{1}{4}\).

Giải thích

Hướng dẫn giải:

Đáp án đúng là: C

cos10°×cos30°×cos50°×cos70°

= \(cos10^\circ \cdot cos30^\circ \cdot \frac{1}{2}\left[ {cos\left( {50^\circ - 70^\circ } \right) + cos\left( {50^\circ + 70^\circ } \right)} \right]\)

\( = cos10^\circ \cdot \frac{{\sqrt 3 }}{2} \cdot \frac{1}{2}\left( {cos20^\circ + cos120^\circ } \right)\)

\( = cos10^\circ \cdot \frac{{\sqrt 3 }}{2} \cdot \frac{1}{2}\left( {cos20^\circ - \frac{1}{2}} \right)\)

\( = \frac{{\sqrt 3 }}{4}cos10^\circ \left( {cos20^\circ - \frac{1}{2}} \right)\)

\( = \frac{{\sqrt 3 }}{4}cos10^\circ cos20^\circ - \frac{{\sqrt 3 }}{8}cos10^\circ \)

\( = \frac{{\sqrt 3 }}{4} \cdot \frac{1}{2}\left[ {cos\left( {10^\circ - 20^\circ } \right) + cos\left( {10^\circ + 20^\circ } \right)} \right] - \frac{{\sqrt 3 }}{8}cos10^\circ \)\( = \frac{{\sqrt 3 }}{4} \cdot \frac{1}{2}\left( {cos10^\circ + cos30^\circ } \right) - \frac{{\sqrt 3 }}{8}cos10^\circ \)

\( = \frac{3}{{16}}\).