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Example 15 Prove that cos (𝜋/4 + x) + cos (𝜋/4 − 𝑥) = root(2) cos 𝑥 Solving L.H.S : cos (𝜋/4 + x) + cos (𝜋/4 − 𝑥) Using 𝑐𝑜𝑠 𝐴+𝐵﷯+𝑐𝑜𝑠 𝐴−𝐵﷯=2𝑐𝑜𝑠 𝐴﷯𝑐𝑜𝑠 𝐵﷯ cos π﷮4﷯+π﷯+cos π﷮4﷯−x﷯=2 cos﷮ π﷮4﷯﷯﷯ cos﷮𝑥﷯ = 2 × 1﷮ ﷮2﷯﷯ cos﷮𝑥﷯ = ﷮2﷯ cos 𝑥 = R.H.S ∴ L.H.S = R.H.S Hence, Proved

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.