How do you verify the identity $sin(90+A)=cosA$ ?

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Answer 1 · 2016-12-21T19:36:26

Expand using the rule $sin(A + B) = sinAcosB + cosAsinB$ .

$sin(90 + A) = cosA$

$sin90cosA + cos90sinA = cosA$

We know, by the unit circle, that $sin90˚ = 1$ and $cos90˚ = 0$ .

$1(cosA) + 0(sinA) = cosA$

$cosA = cosA$

$LHS = RHS$

Identity proved!

Hopefully this helps!

How do you verify the identity sin(90+A)=cosAsin(90+A)=cosA?