Question

The value of \(\frac {tan\ α}{\sqrt {1+tan^2α}}\) is ____ .

• A. \(cos \ α\)
• B. \(sin \ α\)
• C. \(cosec \ α\)
• D. \(sec \ α\)

Answer 1

The Correct Option is B

To solve the problem, we need to evaluate the expression:
$ \frac{\tan \alpha}{\sqrt{1 + \tan^2 \alpha}} $

1. Use Trigonometric Identity:
We know that:
$ 1 + \tan^2 \alpha = \sec^2 \alpha $
So the expression becomes:
$ \frac{\tan \alpha}{\sqrt{\sec^2 \alpha}} = \frac{\tan \alpha}{\sec \alpha} $

2. Express in Terms of Sine and Cosine:
$ \tan \alpha = \frac{\sin \alpha}{\cos \alpha} $
$ \sec \alpha = \frac{1}{\cos \alpha} $
So,
$ \frac{\tan \alpha}{\sec \alpha} = \frac{\frac{\sin \alpha}{\cos \alpha}}{\frac{1}{\cos \alpha}} = \sin \alpha $

Final Answer:
The value of the expression is $ {\sin \alpha} $