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Theorems for Continuity

If cosA+B=0...

Question

If $cos (A + B) = 0$ and $sin (A - B) = 1 / 2$ , then find the value of $A$ and $B$ where $A$ and $B$ are actual angles.

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Solution

Given,
$cos (A + B) = 0$ and $sin (A - B) = 1 / 2$

$cos (A + B) = cos (90^{o})$ and $sin (A - B) = sin (30^{o})$

Since $A, B$ are acute

or, $A + B = 90^{o}$ .....(1) and $A - B = 30^{o}$ ......(2)

Solving from (1) and (2) we get,

$A = 60^{o}$ and $B = 30^{o}$ .

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