Question

If cos a =x/y find the value of tan a

Answer 1

since,
cos A = base / hypotenuse
cos A = x / y
therefore,
in the right triangle,
(perpendicular)^2 + (base)^2 = (hypotenuse)^2
p^2 + x^2 = y^2
p^2 = y^2 - x^2
p = √y^2 - x^2
hence,
Tan A = perpendicular / hypotenuse
tan A = √y^2 - x^2 /y

Answer 2

tana = sina / cosa

=root(1-cos^2a) / cosa

= root (1-x^2/y^2) / (x/y)

={ root (y^2- x^2)/y^2 } / (x/y)

= root(y^2-x^2)/xy

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