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Question Number 97132 by student work last updated on 06/Jun/20

is the formulla of sin^3 ((π/2)+x)=cos^3 x    correct?

$$\mathrm{is}\:\mathrm{the}\:\mathrm{formulla}\:\mathrm{of}\:\mathrm{sin}\:^{\mathrm{3}} \left(\frac{\pi}{\mathrm{2}}+\mathrm{x}\right)=\mathrm{cos}\:^{\mathrm{3}} \mathrm{x}\:\:\:\:\mathrm{correct}? \\ $$

Commented by student work last updated on 06/Jun/20

ans me

$$\mathrm{ans}\:\mathrm{me} \\ $$

Answered by Ar Brandon last updated on 06/Jun/20

sin((π/2)+x)=sin((π/2)−x)=cosx  thus sin^3 ((π/2)+x)=cos^3 x

$$\mathrm{sin}\left(\frac{\pi}{\mathrm{2}}+\mathrm{x}\right)=\mathrm{sin}\left(\frac{\pi}{\mathrm{2}}−\mathrm{x}\right)=\mathrm{cosx} \\ $$$$\mathrm{thus}\:\mathrm{sin}^{\mathrm{3}} \left(\frac{\pi}{\mathrm{2}}+\mathrm{x}\right)=\mathrm{cos}^{\mathrm{3}} \mathrm{x} \\ $$

Commented by student work last updated on 06/Jun/20

thanks

$$\mathrm{thanks} \\ $$

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