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If tantheta=sqrt(n), where n in N ,geq2...

If `tantheta=sqrt(n),` where `n in N ,geq2,t h e nsec2theta` is always a rational number (b) an irrational number a positive integer (d) a negative integer

A

a rational number

B

an irrational number

C

a positive integer

D

a negative integer.

Text Solution

Verified by Experts

The correct Answer is:
A
`tan theta=sqrt(n)`
`rArr cos 2theta=(1-tan^(2)theta)/(1+tan^(2)theta)=(1-n)/(1+n)` =rational
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