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Which of the following pairs is correct for trigonometric inter-relationships?
$1. \cos \theta$ $a. \frac{\cos \theta}{\sin \theta}$
$2. \tan \theta$ $b. \frac{1}{\csc \theta}$
$3. \cot \theta$ $c. \frac{1}{\sec \theta}$
$4. \sin \theta$ $d. \frac{1}{\cot \theta}$
$e. \sin \theta \cdot \cos \theta$

Prove that,$(\sin \alpha+\cos \alpha)(\tan \alpha+\cot \alpha)=\sec \alpha+\operatorname{cosec} \alpha$

Write 'True' or 'False' and justify your answer.
$\cos \theta = \frac{a^{2} + b^{2}}{2ab}$,where $a$ and $b$ are two distinct numbers such that $ab > 0$.

If $\sec \theta = \frac{5}{3}$,then $\tan \theta = \ldots$

$\sin (45^{\circ}+\theta)-\cos (45^{\circ}-\theta)$ is equal to

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