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  4. If cot θ=(24/7) and θ is not in the first quadrant, then find the value of tan θ- sec θ.

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Q. If $\cot \theta=\frac{24}{7}$ and $\theta$ is not in the first quadrant, then find the value of $\tan \theta-\sec \theta$.

Trigonometry

Solution:

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Given, $\cot \theta=\frac{24}{7}$
As $\tan \theta$ is positive and $\theta \notin Q_1$,
$\theta \in Q_{4-} $
$\therefore \sec \theta=-\frac{25}{24} $
$\tan \theta=\frac{7}{24}$
Now $\tan \theta-\sec \theta=\frac{7}{24}+\frac{25}{24}$
$=\frac{32}{24}=\frac{4}{3}$