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