(A) Given $A + B = \pi / 2$,we have $B = \pi / 2 - A$.Substituting this into the expression,we get $\cos A \cos B = \cos A \cos(\pi / 2 - A) = \cos A

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(A) Given $A + B = \pi / 2$,we have $B = \pi / 2 - A$.Substituting this into the expression,we get $\cos A \cos B = \cos A \cos(\pi / 2 - A) = \cos A \sin A$.Multiplying and dividing by $2$,we get $\frac{1}{2} (2 \sin A \cos A) = \frac{1}{2} \sin(2A)$.Let $f(A) = \frac{1}{2} \sin(2A)$.The maximum value of the sine function $\sin(2A)$ is $1$.Therefore,the maximum value of $f(A) = \frac{1}{2} (1) = 1/2$.

Class 11 Mathematics Trigonometrical Ratios, Functions and Identities Maximum and minimum values of trigonometrical functions, Conditional trigonometrical identities

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If $A + B = \pi / 2$,then the maximum value of $\cos A \cos B$ is:

A
$1/2$
B
$3/4$
C
$1$
D
$4/3$

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Trigonometrical Ratios, Functions and Identities

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Maximum and minimum values of trigonometrical functions, Conditional trigonometrical identities

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If $A + B = \pi / 2$,then the maximum value of $\cos A \cos B$ is:

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