1.

The number of solution the equation `cos(theta)cos(pitheta)=1`has0 (b)2 (c) 4(d) 2

Answer» Correct Answer - C
`cos (theta) cos (pi theta)=1`
`rArr cos (theta)=1 and cos (pi theta)=1` ...(i)
or `cos (theta) =-1 and cos (pi theta)=-1` ...(ii)
If `cos (theta)=1 rArr theta=2 mpi`
and `cos (pi theta) =1 rArr theta =2k, k in Z`
which is possible only when `theta=0`.
Equation (ii) is not possible for any `theta` as for `cos (theta)=-1, theta` should be odd multiple of `pi`, i.e., irrational and for `cos(pi theta)=-1, theta` should be odd integer, i.e., rational.
Both the conditions cannot be satisfied.
Therefore, `theta=0` is the only solution.


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