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What is the maximum value of the expression?

f(n)=5\sin\left (x+\frac{\pi}{4} \right )+3\cos\left (x+\frac{\pi}{4} \right )

  • Option 1)

    4

  • Option 2)

    4\sqrt2

  • Option 3)

    \sqrt{34}

  • Option 4)

    none of these

 

Answers (1)

best_answer

As we learnt

 

Maximum and minimum values -

 

Max. value = \sqrt{a^{2}+b^{2}}

Min. value = -\sqrt{a^{2}+b^{2}}

- wherein

The maximum and minimum value of a\cos \Theta + b\sin \Theta

 

 f(n)=5\left ( \frac{\sin x}{\sqrt2} +\frac{\cos x}{\sqrt2} \right )+3 \left (\frac{\cos x}{\sqrt2}- \frac{\sin x}{\sqrt2} \right )

=\sqrt2\sin x+4\sqrt2\cos x

Max value =\sqrt{\sqrt2^{2}+4\sqrt2^{2}}=\sqrt{\34}

 


Option 1)

4

Option 2)

4\sqrt2

Option 3)

\sqrt{34}

Option 4)

none of these

Posted by

Himanshu

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