prove that maximum value of \(\displaystyle{\cos{\alpha}}{\cos{\beta}}\) occurs

Averie Ferguson

Averie Ferguson

Answered question

2022-03-31

prove that maximum value of cosαcosβ occurs when α=β=σ2
If α,β(0,π2) and α+β=σ(constant), then prove that maximum value of cosαcosβ occurs when α=β=σ2

Answer & Explanation

Janessa Foster

Janessa Foster

Beginner2022-04-01Added 12 answers

Hint:
As α+β=σ (constant), cos(α+β)=cos(σ)= (constant)
So, we need to maximize cos(α-β)

German Ferguson

German Ferguson

Beginner2022-04-02Added 18 answers

cosαcosβ=cos(α+β)+cos(αβ)2=cosσ+cos(σ2β)2
Hence, it is maximized when β=σ2 so that cos(σ2β)=1

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