Question

If \(\sin \theta = \frac{1}{\sqrt{2}}\), then the value of \(3 \sin^2 \theta - 4 \sin^3 \theta \cdot \cos \theta\) is

• A. \(\frac{1}{2}\)
• B. 1
• C. \(\frac{3}{2}\)
• D. 3

Hint:

When working with trigonometric functions, always square the sine and cosine values to simplify the expressions.

Answer 1

The Correct Option is A

We know that \(\sin \theta = \frac{1}{\sqrt{2}}\). Therefore, \(\sin^2 \theta = \frac{1}{2}\). Substitute this into the given expression: \[ 3 \cdot \sin^2 \theta - 4 \cdot \sin^3 \theta \cdot \cos \theta = 3 \cdot \frac{1}{2} - 4 \cdot \frac{1}{2} \cdot \frac{1}{2} = \frac{3}{2} - 1 = \frac{1}{2} \] Thus, the correct answer is \(\frac{1}{2}\).