Çözüldü Trigonometric Identities - Pythagorean Theorem

If, for an ABC right triangle, D is a point on the [BC] edge between the vertices B and C so that |AD| = |CD|, and the tangent value of the acute angles in the ACD triangle is 3 / 4, what is the sine value of the obtuse angle in the ACD triangle?
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∡DAC = ∡DCA = θ
∡ADC = α = 180° - 2θ ⇒ θ = 90° - α / 2 ⇒ tan(θ) = tan(90° - α / 2) = cot(α / 2) = 3 / 4 ⇒ tan(α / 2) = 4 / 3....(I)
For the right triangle based on the equation (I), by Pythagorean Theorem;
sin(α / 2) = 4 / √(3^2 + 3^2) = 4 / 5....(II)
cos(α / 2) = 3 / √(3^2 + 3^2) = 3 / 5....(III)
Using the equations (II) and (III) for the trigonometric identity sin(α) = 2·sin(α / 2)·cos(α / 2);
sin(α) = 2·(4 / 5)·(3 / 5) = 24 / 25