Question

tan(x) * tan(y) = 1, Which of the following values of x and y satisfy the given equation.

Answer 1

it is your questions answer

Answer 2

Given :  tan(x)  tan(y) = 1

To Find :  values of x and y satisfying the condition

Solution

tan(x)  tan(y) = 1

=> tan(x)  = 1/ tan(y)

=> tan(x) = cot y

=>  tan(x) = tan ( π/2 - y)

=> x =   π/2 - y     or nπ + π/2 - y   ( generalized)

=> x + y = π/2     or x + y = nπ + π/2   ( generalized)

 x + y = nπ + π/2

Few examples satisfying it :

x = 30° , y = 60°

x =20° , y = 70°

x = 45° , y = 45°

another method

tan(x)  tan(y) = 1

=> (sinx /cosx) (siny/cosy) = 1

=> sinxsiny = cosxcosy

=> cosxcosy - sinxsiny = 0

=> cos(x + y) =  0

=> x + y  = nπ + π/2

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