In the given figure, $A B$ is the diameter of the circle and the chords $A C = B C$ . Find the value of $\frac{(1 + t a n A)}{(1 + t a n B)}$

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Solution

Now, since $A B = B C$ therefore the triangle ABC is an isosceles triangle.

AB is diameter which means
So, $∠ A C B = 90^{o}$ [Angle in a semicircle]
$∠ A = ∠ B$ [Isosceles triangle ABC] → (i)

From (i) we have,
$t a n A = t a n B$

Therefore putting the values in the expression we have,

$= \frac{(1 + t a n A)}{(1 + t a n B)} = \frac{(1 + t a n A)}{(1 + t a n A)} = 1$

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