Question

IF TAN A=X TAN B=Y PROVE THAT 1/X^2-1/Y^2=1

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

Apply,

tan (A+B) = [tan (A) + tan (B)]/(1-tan (A)*tan (B))

putting given values,

tan (A+B)= (x/x+1 +1/2x+1)/(1-x/(x+1)(2x+1))

or,

tan (A+B) = (x(2x+1)+x+1)/[(x+1)*(2x+1)-x]

Value of both numerator and denominator on R.H.S. are equal hence,

tan (A+B) = 1

or

A+B = 45.