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  • The maximum value of <img alt="4^{\cot\theta }\times 8^{\tan\theta }" src="https://entrancecorner.oncodecogs.com/gif.latex?4%5E%7B%5Ccot%5Ctheta%20%7D%5Ctimes%208%5E%7B%5Ctan%5Ctheta%20%7

The maximum value of 4^{\cot\theta }\times 8^{\tan\theta }  is

 

Option: 1

\sqrt{13}


Option: 2

-\sqrt{13}


Option: 3

\sqrt{14}


Option: 4

-\sqrt{14}


Answers (1)

best_answer

Given that,

4^{\cot\theta }\times 8^{\tan\theta }

The formula to find the maximum value,

a\sin \theta +b\cos\theta =\sqrt{a^{2}+b^{2}}

Therefore,

4^{\cot\theta }\times 8^{\tan\theta }=2^{2\cot\theta }\times2^{3\tan\theta }
2\cot\theta+3\tan\theta=\sqrt{2^{2}+3^{2}}

  2\cot\theta+3\tan\theta=\sqrt{13}

 

Posted by

Ajit Kumar Dubey

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