If in a triangle a = √3+1,b=√3−1,C=60∘ then the value of A is ?
A
75∘
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B
90∘
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C
105∘
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D
120∘
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Solution
The correct option is C105∘ A+B+C=180∘ A+B=120∘ .... (1) From law of tangent, we know that tan (A−B2)=a−ba+bcotC2 =(√3+1)−(√3−1)(√3+1)+(√3−1)cot30∘ =22√3cot30∘ tan(A−B2)=1 A−B=90∘ ..... (2) By equation 1 & 2, we get A=105∘