Question:
If \(\tan \theta – \cot \theta = 0\), then find the value of \(\sin \theta \cdot \cos \theta\).
यदि \(\tan \theta – \cot \theta = 0\) है, तो \(\sin \theta \cdot \cos \theta\) का मान ज्ञात कीजिए।
Options:
- 0
- 1
- 1/2
- 1/4
- 0
- 1
- 1/2
- 1/4
Correct Answer: c)
Explanation:
\(\tan \theta = \cot \theta \implies \tan^2 \theta = 1 \implies \theta = 45^\circ\).
\(\sin 45^\circ \cdot \cos 45^\circ = \dfrac{1}{\sqrt{2}} \times \dfrac{1}{\sqrt{2}} = \dfrac{1}{2}\).
\(\tan \theta = \cot \theta \implies \theta = 45^\circ\)।
\(\sin 45^\circ \cdot \cos 45^\circ = \dfrac{1}{\sqrt{2}} \times \dfrac{1}{\sqrt{2}} = \dfrac{1}{2}\)।