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Question Number 200823 by mathlove last updated on 24/Nov/23

$$cos20\cdot cos40+{cos}^{2}80=?$$

Answered by som(math1967) last updated on 24/Nov/23

$$\frac{1}{2}(2cos20cos40+2{cos}^{2}80)$$$$=\frac{1}{2}(cos20+cos60+1+cos160)$$$$=\frac{1}{2}(cos20+\frac{1}{2}+1-cos20)$$$$=\frac{1}{2}\times \frac{3}{2}=\frac{3}{4}$$

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