KVPY SX SB Exam 2018 Question Paper

Cos x + cos( $\sqrt{2}$ x) will always be less than 2 except when both cos x = 1 & cos ( $\sqrt{2}$ x) = 1
cos x = 1 ⇒ x = 2nπ
cos ( $\sqrt{2}$ x) = 1 ⇒ x = 2 mπ
both can simultaneously be 1 only when x = 0
⇒ S = R – {0}