Question

Write the expression as either the sine, cosine, or tangent of a single angle.

cosine of pi divided by three times cosine of pi divided by five plus sine of pi divided by three times sine of pi divided by five.

Answer 1

Answer on Question #48678 – Math – Trigonometry

Write the expression as either the sine, cosine, or tangent of a single angle.

cosine of pi divided by three times cosine of pi divided by five plus sine of pi divided by three times sine of pi divided by five.

Solution.

$$\cos \frac {\pi}{3} \cdot \cos \frac {\pi}{5} + \sin \frac {\pi}{3} \cdot \sin \frac {\pi}{5} = \cos \left(\frac {\pi}{3} - \frac {\pi}{5}\right) = \cos \frac {5 \pi - 3 \pi}{1 5} = \cos \frac {2 \pi}{1 5}.$$

Answer: $\cos \frac{2\pi}{15}$ .

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