JEE Advance - Mathematics (1994 - No. 25)
If $$x$$ is not an integral multiple of $$2\pi $$ use mathematical induction to prove that :
$$$\cos x + \cos 2x + .......... + \cos nx = \cos {{n + 1} \over 2}x\sin {{nx} \over 2}\cos ec{x \over 2}$$$
The statement is false for all values of x.
The statement is true for all values of x.
The statement can be proven using mathematical induction.
The statement cannot be proven using mathematical induction.
Mathematical induction is not applicable in this case.