Question

Which expression is equal to –1? cot StartFraction pi Over 4 EndFraction sin StartFraction pi over 2 EndFraction sin StartFraction 3 pi Over 2 EndFraction tan StartFraction 5 pi Over 4 EndFraction

Answer 1

Given:

The four expression in the options.

To find:

Which expression is equal to –1.

Solution:

In option A,

$\cot \left(\dfrac{\pi}{4}\right)=1$

In option B,

$\sin \left(\dfrac{\pi}{2}\right)=1$

In option C,

$\sin \left(\dfrac{3\pi}{2}\right)=\sin \left(\pi+\dfrac{\pi}{2}\right)$

$\sin \left(\dfrac{3\pi}{4}\right)=-\sin \left(\dfrac{\pi}{2}\right)$   $[\because \sin(\pi+\theta)=-\sin \theta]$

$\sin \left(\dfrac{3\pi}{4}\right)=-1$

In option D,

$\tan \left(\dfrac{5\pi}{4}\right)=\tan \left(\pi+\dfrac{\pi}{4}\right)$

$\tan \left(\dfrac{5\pi}{4}\right)=\tan \left(\dfrac{\pi}{4}\right)$   $[\because \tan(\pi+\theta)=\tan \theta]$

$\tan \left(\dfrac{5\pi}{4}\right)=1$

Therefore, the correct option is C.