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10. Find measure of the angles A and B. if cos(A-B)=and sin(A + B)2 |
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Answer» We know thatsin60^{\circ}=\FRAC{\sqrt{3}}{2}SIN60 ∘ = 23 cos30^{\circ}=\frac{\sqrt{3}}{2}cos30 ∘ = 23 USING the valuescos(A-B)=cos30^{\circ}cos(A−B)=cos30 ∘ A-B=30A−B=30 ...(1)SIN(A+B)=sin60^{\circ}sin(A+B)=sin60 ∘ A+B=60A+B=60 ...(2)Adding equation (1) and (2) we get2A=902A=90A=45^{\circ}A=45 ∘ Substitute the value of A in equation (1)45-B=3045−B=30B=45-30=15^{\circ}B=45−30=15 ∘ Hence, the measure of anglesA=45^{\circ}A=45 ∘ and B=15^{\circ}B=15 ∘ |
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