Answer:
Options (2), (4) and (5)
Step-by-step explanation:
An angle whose measure is [tex]\frac{3\pi }{4}[/tex] terminates in quadrant 2 and its reference angle is [tex]\frac{\pi}{4}[/tex].
As we know only Sine value of a reference angle which terminates in 2nd quadrant is positive. Tan and Cosine of this angle are negative.
Similarly, Cosec of a reference angle terminating in 2nd quadrant is positive while sec and cot values of the same angle are negative in the 2nd quadrant.
[tex]\text{Cosec}(\frac{3\pi}{4})=\text{Cosec}(\frac{\pi}{4})=\sqrt{2}[/tex]
[tex]\text{Sec}\frac{3\pi}{4}=-\text{Sec}\frac{\pi}{4}=-\sqrt{2}[/tex]
[tex]\text{Cot}(\frac{3\pi}{4})=-\text{Cot}(\frac{\pi}{4} )=-1[/tex]
Therefore, Options (2), (4) and (5) will be the answer.
