tan(x) * tan(y) = 1, Which of the following values of x and y satisfy the given equation.
Answers
it is your questions answer
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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