Question

Which of the following pair is a correct trignometric inter-relationship?

(1) $\cos \theta$	(a) $\frac{1}{\tan \theta }$
(2) $\tan \theta$	(b) $\frac{1}{co\sec \theta }$
(3) $\cot \theta$	(c) $\frac{1}{\sec \theta }$
(4) $\sin \theta$	(d) $\frac{1}{\cot \theta }$

• A. $1-d,2-e,3-b,4-a$
• B. $1-b,2-a,3-e,4-d$
• C. $1-c,2-d,3-a,4-b$
• D. $1-e,2-b,3-c,4-d$

Answer 1

The correct option is C $1-c,2-d,3-a,4-b$

We can write $\cos \theta$ as $\frac{1}{\frac{1}{\cos \theta }}=\frac{1}{\sec \theta }$

$\therefore \cos \theta =\frac{1}{\sec \theta }$ .......... $\left(1\right)$

Now, $\tan \theta =\frac{\sin \theta }{\cos \theta }=\frac{1}{\frac{\cos \theta }{\sin \theta }}=\frac{1}{\cot \theta }$

$\therefore \tan \theta =\frac{1}{\cot \theta }$ ........ $\left(2\right)$

$\cot \theta =\frac{1}{\tan \theta }$ ............ $\left(3\right)$

$\sin \theta =\frac{1}{\frac{1}{\sin \theta }}=\frac{1}{\text{cosec}\theta }$ ...... $\left(4\right)$

Hence, the correct answer is $1-c,2-d,3-a,4-b$