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Two sharp angles a and B are known simultaneously: (1) a + 2B = 120 (2) Tan (A / 2) * Tan B = 2-radical 3. Find the value of a and B
A/2+B=60°,tan(A/2+B)=tan60°=√3,tan(A/2+B)=[tan(A/2)+tanB]/[1-tan(A/2)*tanB]=[tan(A/2)+tanB]/[1-(2-√3)]tan(A/2)+tanB=√3(√3-1),tan(A/2)+tan(60°-A/2)=3-√3,tan(A/2)+[tan60°-tanA/2]/[1-tan60°tanA...
Given that a and B are acute angles, cosa = 1 / 5, Tan (a-b) = - 1 / 3, find CoSb
∵ a, B is an acute angle ∵ A-B ∈ (- π / 2, π / 2), Sina > 0 ∵ Tan (a-b) = - 1 / 3 [sin (a-b)] ^ 2 + [- 3Sn (a-b)] ^ 2 = 1 ∵ sin (a-b) = 1 / √ 10, con (a-b) = - 3 / √ 10 ∵ cosa = 1 / 5 ∵ Sina = √ [1 - (COSA) ^ 2] = 2 √ 6 / 5, so CoSb = cos [a - (a-b)] = cosacos (a-b) + sinasin (a-b) = (1
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