How do you verify the identity $cos^2beta+cos^2(pi/2-beta)=1$ ?

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Answer 1 · 2017-01-16T05:39:45

See the proof below

$cos(pi/2)=0$

$sin(pi/2)=1$

$cos(pi/2-beta)=cos(pi/2)cosbeta+sin(pi/2)sinbeta$

$=0+sinbeta$

Therefore,

$LHS=cos^2beta+cos^2((pi/2)-beta)$

$=cos^2beta+sin^2beta=1=RHS$

$QED$

How do you verify the identity cos^2beta+cos^2(pi/2-beta)=1cos^2beta+cos^2(pi/2-beta)=1?