Question

Let α = $2f(x)3f(x)$ &

β=$f(x) = \cos\lbrack\pi^{2}\rbrack x + \cos\lbrack - \pi^{2}\rbrack x,f\left( \frac{\pi}{4} \right) = 2$then-

• A. α = β
• B. α<β
• C. 4α – 3β = 0
• D. 3α – 4β = 0

Answer 1

Answer: (D)

3α – 4β = 0

Answer 2

α = = $\frac { 1 } { 3 }$

β = – $\frac { 1 ^ { 2 } + 2 ^ { 2 } + \ldots . . + \mathrm { n } ^ { 2 } } { \mathrm { n } ^ { 4 } }$

= $\frac { 1 } { 4 }$ – 0 = $\frac { 1 } { 4 }$

∴ 3α – 4β = 3 × $\frac { 1 } { 3 }$ – 4 × $\frac { 1 } { 4 }$= 1 – 1 = 0