Correct Answer - Option 2 : 1
Given :-
ΔABC is a right angle at B
sin A = (1/√2)
Concept :-
As sin A = (1/√2)
sin A = sin45°
A = 45°
Calculation :-
As B is right angle and,
⇒ ∠A = 45°
Sum of triangle = 180°
⇒ ∠A + ∠B + ∠C = 180°
⇒ 45° + 90° + ∠C = 180°
⇒ ∠C = 180° - 135°
⇒ ∠C = 45°
As ∠A = ∠C = 45°
⇒ sin A = cos C = cos A = (1/√2)
ΔABC is an isosceles triangle
Now, Put the value of all identities
⇒ \(\frac{sin A(cos C + cos A)}{cos C (sin C + sin A)}\) = (sin A (sin A + sin A))/(sin A (sin A + sin A))
⇒ \(\frac{sin A(cos C + cos A)}{cos C (sin C + sin A)}\) = 1
∴ \(\frac{sin A(cos C + cos A)}{cos C (sin C + sin A)}\) = 1
