Question

Let f(x) = sin + cos , {.} denotes the fraction part. Then the set of values of a, for which f(x) can attain its maximum value is –

• A. (0,4/p)
• B. (p/4, )
• C. (0, )
• D. ) None

Answer 1

)

Sol. \ f(x) = sin q + cos q = $\sqrt { 2 }$ sin $\left( \frac { \pi } { 4 } + \theta \right)$

maximum value at q = $\frac { \pi } { 4 }$

\ = $\frac { \pi } { 4 }$ Ž {x} = $\frac { \pi \mathrm { a } } { 4 }$

Q 0 £ $\frac { \pi \mathrm { a } } { 4 }$< 1 Ž

Ž a Ī $\left( 0 , \frac { \pi } { 4 } \right)$ Q a ¹ 0