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EXAMPLE 17 If a and B are acute angles such that tan o -m-and tan βm +1and tan p 2m+1P2m +1, prove that |
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Answer» we know that tan(a+b) = (tan(a)+tan(b))/(1-tan(a)tan(b)) = [m/(m+1) + 1/(2m+1)]/[1-m/(m+1)(2m+1)] = [2m²+m+m+1/(m+1)(2m+1)]/[(2m²+3m+1-m)/(m+1)(2m+1)]= 2m²+2m+1/2m²+2m+1= 1 so. tan(a+b) = 1=> a+b = tan-¹(1) = π/4.. |
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