Question

If \( \sin \theta = \frac{3}{5} \) and \( \theta \) is not in the first quadrant, then \( 15 \sin 2\theta - 20 \cos 2\theta - 7 \tan 2\theta \) is:

• A. -4
• B. -12
• C. 12
• D. 4

Hint:

To solve trigonometric equations, use double angle identities and the Pythagorean identity to find the required values.

Answer 1

The Correct Option is D

We are given that \( \sin \theta = \frac{3}{5} \), and we need to find \( 15 \sin 2\theta - 20 \cos 2\theta - 7 \tan 2\theta \). Step 1: Use the identity for \( \sin 2\theta \), \( \sin 2\theta = 2 \sin \theta \cos \theta \), and \( \cos^2 \theta = 1 - \sin^2 \theta \) to find \( \cos \theta \). Step 2: Using the given value for \( \sin \theta \), calculate \( \cos 2\theta \) and \( \tan 2\theta \). Step 3: Substitute these values into the expression \( 15 \sin 2\theta - 20 \cos 2\theta - 7 \tan 2\theta \) to simplify and find the final value. After the calculations, we find the value of the expression is 4. Thus, the correct answer is 4.