(A) Given $A + B = \frac{\pi}{2}$,we have $B = \frac{\pi}{2} - A$.Let $f(A) = \cos A \cos B = \cos A \cos(\frac{\pi}{2} - A) = \cos A \sin A$.We can r

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(A) Given $A + B = \frac{\pi}{2}$,we have $B = \frac{\pi}{2} - A$.Let $f(A) = \cos A \cos B = \cos A \cos(\frac{\pi}{2} - A) = \cos A \sin A$.We can rewrite this as $f(A) = \frac{1}{2} \sin(2A)$.To find the maximum value,we know that the maximum value of $\sin(2A)$ is $1$.Therefore,the maximum value of $f(A) = \frac{1}{2} \times 1 = \frac{1}{2}$.

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

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If $A + B = \frac{\pi}{2}$,what is the maximum value of $\cos A \cos B$?

A
$\frac{1}{2}$
B
$\frac{3}{4}$
C
$1$
D
$\frac{4}{3}$

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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 $A + B = \frac{\pi}{2}$,what is the maximum value of $\cos A \cos B$?

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