13. which of these has a different value from the others? a tan(3π/4) b sec(π) c cos(3π) d cot(5π/4)

Explanation:

Step1: Calculate value of A

Recall $\tan(\frac{3\pi}{4})=\tan(\pi - \frac{\pi}{4})=-\tan(\frac{\pi}{4})=- 1$.

Step2: Calculate value of B

Recall $\sec(\pi)=\frac{1}{\cos(\pi)}=\frac{1}{-1}=-1$.

Step3: Calculate value of C

Recall $\cos(3\pi)=\cos(2\pi+\pi)=\cos(\pi)=-1$.

Step4: Calculate value of D

Recall $\cot(\frac{5\pi}{4})=\cot(\pi+\frac{\pi}{4})=\cot(\frac{\pi}{4}) = 1$.

Answer:

D. $\cot(\frac{5\pi}{4})$