hyunmin2019314 hyunmin2019314

28-08-2016
Mathematics

contestada

Can some one help explain how to evaluate the following without a calculator?

sin^2(25) sin^2(65)

Respuesta :

dalendrk dalendrk

28-08-2016

We know:
[tex]\sin(90^o-\alpha)=\cos\alpha[/tex]

[tex]\sin25^o=\sin(90^o-65^o)=\cos65^o\ therefore\ \sin^225^o=\cos^265^o[/tex]

We have:
[tex]\sin^225^o+\sin^265^o=\cos^265^o+\sin^265^o=1[/tex]

Used: [tex]\sin^2\alpha+\cos^2\alpha=1[/tex]

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