If sin ( A - B )=frac{1}{2}, cos ( A + B )=frac{1}{2}, 0^{circ} < A + B ≤ 90^{circ}, A > B ,

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8. Introduction to Trigonometry

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If $\sin ( A - B )=\frac{1}{2}, \cos ( A + B )=\frac{1}{2}, 0^{\circ} < A + B \leq 90^{\circ}, A > B ,$ find $A$ and $B$

Option A

Option B

Option C

Option D

Solution

since, $\sin ( A – B )=\frac{1}{2},$ therefore, $A – B =30^{\circ}$ ……$(1)$

Also, since $\cos ( A + B )=\frac{1}{2},$ therefore, $A + B =60^{\circ}$ ……$(2)$

Solving $(1)$ and $(2),$ we get $: A=45^{\circ}$ and $B=15^{\circ} .$

Standard 10

Mathematics

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