Question

The value of sin B − cos A is ______.

Options

• `1/2`

• 1

• 0

• none of these

Answer 1

The value of sin B − cos A is 0.

Explanation:

In right-angled triangle ABC with ∠C = 90°, hypotenuse AB = 5 and perpendicular AC = 3. The base \[\text{BC}$ is $\sqrt{5^2 - 3^2} = 4\].

• \[\sin B = \frac{\text{AC}}{\text{AB}} = \frac{3}{5}\]
• \[\cos A = \frac{\text{AC}}{\text{AB}} = \frac{3}{5}\] (since side AC is adjacent to angle A)

Thus, \[\sin B - \cos A = \frac{3}{5} - \frac{3}{5} = 0\].