Question

Match the terms of Column I with the terms of Column II and choose the correct option from the codes given below.

Column I		Column II
A	$ \sin \frac{25 \pi}{3}$	1	$-\sqrt{3}$
B	$ \cos \frac{41 \pi}{4}$	2	$\frac{\sqrt{3}}{2}$
C	$\tan \left(\frac{-16 \pi}{3}\right)$	3	$1$
D	$ \cot \frac{29 \pi}{4}$	4	$\frac{1}{\sqrt{2}}$

• A. A - (2), B -(4), C - (1), D - (3)
• B. A - (2), B -(1), C - (4), D - (3)
• C. A - (3), B -(1), C - (4), D - (2)
• D. A - (3), B -(4), C - (1), D - (2)

Answer 1

Answer: (A)

A. $\sin \frac{25 \pi}{3}=\sin \left(8 \pi+\frac{\pi}{3}\right)=\sin \frac{\pi}{3}=\frac{\sqrt{3}}{2}$
$[\because \sin (2 n \pi+\theta)=\sin \theta]$
B. $\cos \frac{41 \pi}{4}=\cos \left(10 \pi+\frac{\pi}{4}\right)=\cos \frac{\pi}{4}=\frac{1}{\sqrt{2}}$
$[\because \cos (2 n \pi+\theta)=\cos \theta]$
C. $\tan \left(\frac{-16 \pi}{3}\right)=-\tan \frac{16 \pi}{3} [\because \tan (-\theta)=-\tan \theta]$
$=-\tan \left(5 \pi+\frac{\pi}{3}\right)=-\tan \frac{\pi}{3}=-\sqrt{3}$
$[\because \tan (n \pi+\theta)=\tan \theta]$
D. $\cot \frac{29 \pi}{4}=\cot \left(7 \pi+\frac{\pi}{4}\right)=\cot \frac{\pi}{4}=1$
$[\because \cot (n \pi+\theta)=\cot \theta]$
$\therefore A \leftrightarrow 2, B \leftrightarrow 4, C \leftrightarrow 1, D \leftrightarrow 3$