If $$\theta $$ and $$\delta $$ be the latitude of a place and declination of a star respectively, the upper culmination of the star will be north of zenith if its zenith distance, is

If $$\theta $$ and $$\delta $$ be the latitude of a place and declination of a star respectively, the upper culmination of the star will be north of zenith if its zenith distance, is Correct Answer $$\delta - \theta $$

Bissoy MCQ

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Evaluate the following:
$$\frac{{\cos 2\theta \cdot \cos 3\theta - \cos 2\theta \cdot \cos 7\theta + \cos \theta \cdot \cos 10\theta }}{{\sin 4\theta \cdot \sin 3\theta - \sin 2\theta \cdot \sin 5\theta + \sin 4\theta \cdot \sin 7\theta }}$$
The value of $$\frac{{\sec \theta \left( {1 - \sin \theta } \right)\left( {\sin \theta + \cos \theta } \right)\left( {\sec \theta + \tan \theta } \right)}}{{\sin \theta \left( {1 + \tan \theta } \right) + \cos \theta \left( {1 + \cot \theta } \right)}}$$        is equal to:
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If θ and δ be the latitude of an observer and declination of a heavenly body respectively, the upper culmination of the body will be south of zenith if its zenith distance, is
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