By definition we know thaycos(x)=frace^ix+e^-ix2sofrace^ix+e^-ix2=2\e^ix+e^-ix=4now let's multiply both sides by e^ix e^ix^2+1=4e^ixset e^ix=u và you ...

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displaystyle extno solution Explanation: displaystyle extnote that -1lecosxle1displaystyleRightarrowcosx=3 ext is not valid
Given that displaystylecosx=p find an expression, in terms of displaystylep , for displaystyle an^2x ?
displaystyle an^2x=frac1-p^2p^2 Explanation:If cos x =p,displaystylesinx=sqrt1-p^2 rã x =displaystylefracsqrt1-p^2p ...
Indeed, f_A,B(a,b)=(2pi)^-1mathbf 1_0lt alt1mathbf 1_0lt blt2pi and (X,Y)=(Acos B,Asin B) has density f_X,Y where, for every (x,y), f_X,Y(x,y)=(2pi)^-1(x^2+y^2)^-1/2mathbf 1_0lt x^2+y^2lt1 ...

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eginalign*sin (2x)=0 &Longrightarrow 2x=kpi o x=frackpi2\ cos x=0&Longrightarrow x= fracpi2+kpi=frac(2k+1)pi2endalign*
sin & cos have period 2pi and an has period pi. When solving an equation, make sure to menu all roots in a period. an x=0implies x=0 in <0,pi), i.e. X=kpi. an x=1implies x=dfracpi4 ...
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left< eginarray l l 2 và 3 \ 5 và 4 endarray ight> left< eginarray l l l 2 & 0 & 3 \ -1 và 1 và 5 endarray ight>

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