Question

If sec A sin A = 0, find the value of cos A.

Answer 1

Given:

sec A sin A = 0

Formula:

\[\sec A = \frac{1}{\cos A} \text{ and } \tan A = \frac{\sin A}{\cos A}\]

Solution:

\[\left(\frac{1}{\cos A}\right) \cdot \sin A = 0\]  [Expressing secant in terms of cosine]

\[\frac{\sin A}{\cos A} = 0\]  [Simplifying the product]

tan A = 0  [Using the tangent identity \[\tan A = \frac{\sin A}{\cos A}\]]

A = 0°  [Finding the angle where tangent is zero for acute angles]

cos A = cos(0°)  [Substituting the value of A into cosine]

cos A = 1  [Using the standard trigonometric value cos(0°) = 1]

∴ cos A = 1