Question

If $\sin \theta = \csc \theta$ and $0 \leq \theta \leq \dfrac{\pi}{2}$, then the value of $\theta$ will be

• A. 0
• B. $\dfrac{\pi}{4}$
• C. $\dfrac{\pi}{2}$
• D. $\pi$

Hint:

For $\sin \theta = \csc \theta$, multiply both sides by $\sin \theta$ to form $\sin^2 \theta = 1$. Then solve for $\theta$.

Answer 1

The Correct Option is C

Step 1: Write the given equation.
\[ \sin \theta = \csc \theta = \dfrac{1}{\sin \theta} \] Step 2: Multiply both sides by $\sin \theta$.
\[ \sin^2 \theta = 1 \] \[ \sin \theta = 1 \] Step 3: Find $\theta$.
For $\sin \theta = 1$, within $0 \leq \theta \leq \dfrac{\pi}{2}$, we have $\theta = \dfrac{\pi}{2}$.