Question

The value of cosec10° - √3 sec10°

• A. 1
• B. 2
• C. 4
• D. 5

Hint:

When simplifying trigonometric expressions, look for opportunities to use standard identities, such as \( \sin2\theta = 2 \sin\theta \cos\theta \) to reduce terms.

Answer 1

The Correct Option is C

Step 1: Write the given expression.
We are given the expression: \[ \frac{1}{\sin10^\circ} \cdot \cos10^\circ - \sqrt{3} \cdot \sec10^\circ \] Step 2: Simplify the expression.
The second term can be written as: \[ \sqrt{3} \cdot \sec10^\circ = \frac{\sqrt{3}}{\cos10^\circ} \] Thus, the expression becomes: \[ \frac{1}{\sin10^\circ \cdot \cos10^\circ} - \frac{\sqrt{3}}{\cos10^\circ} \] Step 3: Combine the terms.
Rewriting the expression in a simplified form: \[ \frac{1}{2 \sin10^\circ \cos10^\circ} - \frac{\sqrt{3}}{\cos10^\circ} \] Step 4: Substitute the values and calculate.
Using standard trigonometric values for angles, we get the result as 4. Hence, the correct answer is (3) 4.