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Maths-

General

Easy

Question

$cos space open parentheses x plus pi over 6 close parentheses cos space open parentheses x minus pi over 6 close parentheses element of$

$[- \frac{1}{4}, \frac{1}{4}]$
$[- \frac{3}{4}, \frac{3}{4}]$
$[- \frac{1}{4}, \frac{3}{4}]$
$[- \frac{1}{2}, \frac{1}{2}]$

hint Hint:

In this question, we have to find the range of the given function. For that we will first simplify the equation and later find the range of the simplified equation.

The correct answer is: $open square brackets negative 1 fourth comma 3 over 4 close square brackets$

$cos space open parentheses x plus pi over 6 close parentheses cos space open parentheses x minus pi over 6 close parentheses equals 1 half open square brackets cos open parentheses x plus straight pi over 6 plus x plus straight pi over 6 close parentheses plus cos open parentheses x plus straight pi over 6 minus x plus straight pi over 6 close parentheses close square brackets equals 1 half open square brackets cos space 2 x plus cos straight pi over 3 close square brackets equals 1 half open parentheses cos space 2 x plus 1 half close parentheses equals fraction numerator cos space 2 x over denominator 2 end fraction plus 1 fourth A s comma space minus 1 less or equal than cos space y less or equal than 1 rightwards double arrow negative 1 less or equal than cos space 2 x less or equal than 1 rightwards double arrow fraction numerator negative 1 over denominator 2 end fraction less or equal than fraction numerator cos space 2 x over denominator 2 end fraction less or equal than 1 half fraction numerator negative 1 over denominator 2 end fraction plus 1 fourth less or equal than 1 fourth plus fraction numerator cos space 2 x over denominator 2 end fraction less or equal than 1 half plus 1 fourth fraction numerator negative 1 over denominator 4 end fraction less or equal than 1 fourth plus fraction numerator cos space 2 x over denominator 2 end fraction less or equal than 3 over 4 S o comma space cos space open parentheses x plus pi over 6 close parentheses cos space open parentheses x minus pi over 6 close parentheses element of open square brackets fraction numerator negative 1 over denominator 4 end fraction comma 3 over 4 close square brackets$

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