Let n be a positive integer such thatsin(π2n)+cos(π2n)=√n2
(sin(π2n)+cos(π2n))2=n2
1+2sinπ2ncosπ2n=n4......[cos2θ+sin2θ=1]
⇒1+sinπ2n−1=n4
sin(π2n−1)=n−44 AS n=+ve.≠1 and sinθ≤10<n−44≤1 ∴4<n≤8
Let n be positive integer such that sinπ2n+cosπ2n=√n2. Then
Let n be a positive integer such that sinπ2n+cosπ2n=√n2. Then