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Maths-

General

Easy

Question

Maximum value of $fraction numerator 1 over denominator square root of 7 sin space x plus square root of 29 cos space x plus 7 end fraction$

13
1
$1 / 13$
49

hint Hint:

In the question we have to find the maximum value of the given function. For this we will assume the function as $fraction numerator 1 over denominator g left parenthesis x right parenthesis end fraction$ then we will find the range of g(x) and then the range of the given function.

The correct answer is: 1

$y equals fraction numerator 1 over denominator square root of 7 sin space x plus square root of 29 cos space x plus 7 end fraction g left parenthesis x right parenthesis equals square root of 7 sin space x plus square root of 29 cos space x plus 7 minus square root of a squared plus b squared end root less or equal than a sin x plus b cos x less or equal than square root of a squared plus b squared end root rightwards double arrow negative square root of open parentheses square root of 7 close parentheses squared plus open parentheses square root of 29 close parentheses squared end root less or equal than square root of 7 sin x plus square root of 29 cos x less or equal than square root of open parentheses square root of 7 close parentheses squared plus open parentheses square root of 29 close parentheses squared end root rightwards double arrow negative square root of 36 less or equal than square root of 7 sin x plus square root of 29 cos x less or equal than square root of 36 rightwards double arrow negative 6 less or equal than square root of 7 sin x plus square root of 29 cos x less or equal than 6 rightwards double arrow negative 6 plus 7 less or equal than square root of 7 sin x plus square root of 29 cos x plus 7 less or equal than 6 plus 7 rightwards double arrow 1 less or equal than square root of 7 sin x plus square root of 29 cos x plus 7 less or equal than 13 rightwards double arrow 1 greater or equal than fraction numerator 1 over denominator square root of 7 sin x plus square root of 29 cos x plus 7 end fraction greater or equal than 1 over 13 S o comma space m a x i m u m space v a l u e space o f space t h e space f u n c t i o n space i s space 1.$

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