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Maths-

General

Easy

Question

$cos squared space open parentheses 60 to the power of ring operator plus x close parentheses minus cos squared space open parentheses 60 to the power of ring operator minus x close parentheses element of open square brackets negative m over 2 comma m over 2 close square brackets not stretchy rightwards double arrow straight m equals$

1
3
$- \sqrt{3}$
$\sqrt{3}$

hint Hint:

In this question, we have to find the value of m in $cos squared space open parentheses 60 to the power of ring operator plus x close parentheses minus cos squared space open parentheses 60 to the power of ring operator minus x close parentheses element of open square brackets negative m over 2 comma m over 2 close square brackets$ . For this first we will simplify the given trigonometric function then assume the range of the function to find the range of the given function. Then we will compare the range derived o the range given to find the required value of m.

The correct answer is: $square root of 3$

$space space space space cos squared open parentheses 60 plus x close parentheses minus cos squared open parentheses 60 minus x close parentheses equals open square brackets cos open parentheses 60 plus x close parentheses plus cos space open parentheses 60 minus x close parentheses close square brackets open square brackets cos space open parentheses 60 plus x close parentheses minus cos open parentheses 60 minus x close parentheses close square brackets equals open parentheses 2. cos space 60. cos space x close parentheses open parentheses negative 2. sin 60. sin space x close parentheses equals open parentheses 2.1 half. cos space x close parentheses open parentheses negative 2. fraction numerator square root of 3 over denominator 2 end fraction. sin space x close parentheses equals negative square root of 3. cos space x. sin space x equals negative fraction numerator square root of 3 over denominator 2 end fraction. sin space 2 x space F o r space m a x i m u m space v a l u e space o f space f left parenthesis x right parenthesis comma space sin space 2 x equals 1 f left parenthesis x right parenthesis equals fraction numerator negative square root of 3 over denominator 2 end fraction cross times 1 equals fraction numerator negative square root of 3 over denominator 2 end fraction F o r space m i n i m u m space v a l u e space o f space f space left parenthesis x right parenthesis comma space sin space 2 x space equals negative 1 f left parenthesis x right parenthesis equals fraction numerator negative square root of 3 over denominator 2 end fraction cross times negative 1 equals fraction numerator square root of 3 over denominator 2 end fraction A s space space cos squared open parentheses 60 plus x close parentheses minus cos squared open parentheses 60 minus x close parentheses element of open square brackets fraction numerator negative square root of 3 over denominator 2 end fraction comma fraction numerator square root of 3 over denominator 2 end fraction close square brackets S o comma space m equals square root of 3$

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