Question

Sa se determine masura x a unui unghi ascutit stiind ca:
a) (sin x- cos 78)^2014=0
b) cos^3 x/1-sin^2 x=sin^3 x/1-cos^2 x

Answer 1

 

Se stie ca unghiul x este ascutit.

⇒  x ∈ C1\\

.

$\displaystyle\bf\\a)\\\\\Big(sin~x-cos~78^o\Big)^{2014}=0\\\\\Big(sin~x-cos~78^o\Big)^{2014}=0^{2014}\\\\\implies~sin~x-cos~78^o=0\\\\sin~x=cos~78^o~~~si~x\in C1\\\\sin~x=sin(90^o-78^o)\\\\sin~x=sin~12^o\\\\\implies~\boxed{\bf x=12^o}$

.

$\displaystyle\bf\\b)\\\\cos^3x-sin^2x=sin^3x-cos^2x~~~\Big|\\\\cos^3x+cos^2x=sin^3x+sin^2x\\\\sin^3x=cos^3x~~~si~~~sin^2x=cos^2x~\implies~sinx=cosx\\\\\implies~\boxed{\bf x=45^o}\\\\~\implies~sinx=cosx=\frac{\sqrt{2}}{2}$