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Question Number 80219 by Power last updated on 01/Feb/20

Answered by som(math1967) last updated on 01/Feb/20

$$let\frac{\pi }{7}=\theta$$$$\therefore cos2\theta +cos4\theta +cos6\theta$$$$=\frac{1}{2sin\theta }(2cos2\theta sin\theta +2sin\theta cos4\theta$$$$+2sin\theta cos6\theta )$$$$=\frac{1}{2sin\theta }(sin3\theta -sin\theta +sin5\theta -sin3\theta$$$$sin7\theta -sin5\theta )$$$$\frac{1}{2sin\theta }(sin7\theta -sin\theta )★$$$$=-\frac{1}{2sin\theta }\times sin\theta =-\frac{1}{2}ans$$$$★sin7\theta =sin\pi =0$$

Commented by peter frank last updated on 01/Feb/20

$$great$$

Commented by Power last updated on 02/Feb/20

$$\mathrm{thanks}$$

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