Question

If \(sin \ θ=cos\  θ\) \((0<θ<90°)\), then \(tan\ θ =\) ____ .

• A. -1
• B. 4
• C. 2
• D. 1

Answer 1

The Correct Option is D

To solve the problem, we need to find the value of \( \tan \theta \) given that \( \sin \theta = \cos \theta \), and \( 0^\circ < \theta < 90^\circ \).

1. Using the Identity:
We are given \( \sin \theta = \cos \theta \).
Divide both sides of the equation by \( \cos \theta \) (which is not zero in the given range):
\[ \frac{\sin \theta}{\cos \theta} = \frac{\cos \theta}{\cos \theta} \] \[ \tan \theta = 1 \]

2. Verifying the Angle:
The equality \( \sin \theta = \cos \theta \) occurs at \( \theta = 45^\circ \), where indeed \( \tan 45^\circ = 1 \).

Final Answer:
The value of \( \tan \theta \) is 1.