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What positive value(s) of x, less than 360^o, will give a mini

Question

What positive value(s) of x, less than $36 0^{o}$ , will give a minimum value for 4 - 2 sin x cos x?

\frac{π}{4}

only

\frac{5 π}{4}

only

\frac{π}{2}

and

\frac{5 π}{2}

\frac{3 π}{2}

\frac{π}{4}

and

\frac{5 π}{4}

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What positive value(s) of x, less than

36 0^{o}

, will give a minimum value for 4 - 2 sin x cos x?

10 mins ago

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10 mins ago

Text solutionVerified

$4 - 2 s in x cos x = 4 - s in 2 x$ , It will be minimum if $s in 2 x$ is maximum
The maximum value of $s in 2 x$ is $1$ and occurs at $2 x = 90, 450$
Which implies $x = 45, 225$
Therefore the correct option is $E$

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Question Text	What positive value(s) of x, less than $36 0^{o}$ , will give a minimum value for 4 - 2 sin x cos x?
Answer Type	Text solution:1
Upvotes	150