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soldi70 [24.7K]
3 years ago
12

Explain how to find the exact value of cos(75°).

Mathematics
1 answer:
DanielleElmas [232]3 years ago
4 0

Answer:

\cos(75 \degree)  =  \cos(45 \degree + 30\degree)  \\  \\  =  \cos(45\degree)  \cos(30\degree)  -  \sin(45\degree)  \sin(30\degree)  \\  \\  = ( \frac{1}{ \sqrt{2} } ).( \frac{ \sqrt{3} }{2} ) - ( \frac{1}{ \sqrt{2} } ).( \frac{1}{2} ) \\  \\  =  \frac{ \sqrt{3} }{2 \sqrt{2} }  -  \frac{1}{2 \sqrt{2} }  \\  \\  =  \frac{ \sqrt{3}  - 1}{2 \sqrt{2} }  \\  \\   =  \frac{0.73205}{2.828427}  \\  \\  = 0.2588

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