A=tan inverse of X root 3 by 2k-x and B=tan inverse of 2x-k by k root 3 then A-B =
Answers
A - B = Tan⁻¹( 1/ √3) = 30° if A = Tan⁻¹( x√3 / (2k - x) ) & B = Tan⁻¹( (2x - k) / k√3 )
Step-by-step explanation:
A = Tan⁻¹( x√3 / (2k - x) )
=> TanA = x√3 / (2k - x)
B = Tan⁻¹( (2x - k) / k√3 )
=> TanB = (2x - k) / k√3
Tan (A - B) = (Tan A - TanB) /(1 + TanATanB)
=> Tan (A - B) = ( x√3 / (2k - x) - (2x - k) / k√3 ) / (1 + (x√3 / (2k - x))*(2x - k) / k√3 )
=> Tan (A - B) = (3kx - (2x - k)(2k - x) ) / ( (2k - x) k√3 + x√3(2x - k) )
=> Tan (A - B) = (3kx - 4kx + 2k² + 2x² - kx) / ( 2√3k² - xk√3 + 2√3k² - xk√3)
=> Tan (A - B) = (2k² + 2x² - 2kx) / ( 2√3k² - 2xk√3 + 2√3x²)
=> Tan (A - B) = (k² + x² - kx) / (√3k² - xk√3 + √3x²)
=> Tan (A - B) = (k² + x² - kx) / (√3(k² + x² - kx))
=> Tan (A - B) = 1/√3
=> A - B = Tan⁻¹( 1/ √3)
=> A - B = 30°
Learn More
If tan(a+b)=1 and tan(a-b)=1/√3, then find the value of a and b.
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