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Solution
Given That :-
- tan A = n/(n+1)
- tan B = 1/(2n+1)
Find :-
- Value of tan ( A + B)
Explanation
Using Formula
☛ tan(A + B) = (tan A + tan B )/(1 - tan A tan B)
So, now keep all above values
➥ tan ( A + B ) = [n/(n+1) + 1/(2n+1)]/[(1 - n/(n+1) * 1/(2n+1) ]
➥ tan ( A + B ) = [n*(2n+1)+(n+1)]/[(n+1)(2n+1)] × [(n+1)(2n+1)/(n+1)(2n+1)-n]
cancel (n+1)(2n+1) , by denominator & Numerator
➥ tan ( A + B ) = (2n² + n + n +1) × 1/(2n²+n+2n+1-n)
➥ tan ( A + B ) = (2n²+2n+1)/(2n²+2n+1)
Cancel denominator & Numerator
we got ,
➥ tan ( A + B ) = 1
Hence
- Value of tan (A + B) will be = 1
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