Trigonometric Functions — Maths STD 12 Science — Question

By sine rule,

$\frac{a}{\sin A}=\frac{b}{\sin B}=k$

$\therefore a=k \sin A, b=k \sin B$

$\therefore$ (1) gives, $\frac{\cos A}{k \sin A}=\frac{\cos B}{k \sin B}$

$\therefore \frac{\cos A}{\sin A}=\frac{\cos B}{\sin B}$

∴ sin A cos B = cos A sinB ∴ sinA cosB – cosA sinB = 0 ∴ sin (A – B) = 0 = sin0 ∴ A – B = 0 ∴ A = B ∴ the triangle is an isosceles triangle.