(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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(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

Easy

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
$\frac{4}{3}$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

Trigonometrical Ratios, Functions and Identities

Subtopic

Maximum and minimum values of trigonometrical functions, Conditional trigonometrical identities

The minimum value of the function $f(x) = 2\cos 2x - \cos 4x$ in the interval $0 \le x \le \pi$ is:

Medium

View Solution

If $A+B+C=\pi$ and $\cos B=\cos A \cos C$,then $\tan A \tan C=$

MediumAP EAMCET 2022

View Solution

If $p = \sin^2 \theta + \cos^4 \theta$,then for all real values of $\theta$,which of the following is true?

Difficult

View Solution

The maximum value of $12 \sin x - 5 \cos x + 3$ is

EasyAP EAMCET 2024

View Solution

The maximum value of $\left(2 \cos^2 18^{\circ} - \sin 18^{\circ}\right) \left(\cos \theta + 3 \sqrt{2} \cos \left(\theta + \frac{\pi}{4}\right) + 3\right)$ is

MediumTS EAMCET 2019

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

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

Similar Questions

The minimum value of the function $f(x) = 2\cos 2x - \cos 4x$ in the interval $0 \le x \le \pi$ is:

If $A+B+C=\pi$ and $\cos B=\cos A \cos C$,then $\tan A \tan C=$

If $p = \sin^2 \theta + \cos^4 \theta$,then for all real values of $\theta$,which of the following is true?

The maximum value of $12 \sin x - 5 \cos x + 3$ is

The maximum value of $\left(2 \cos^2 18^{\circ} - \sin 18^{\circ}\right) \left(\cos \theta + 3 \sqrt{2} \cos \left(\theta + \frac{\pi}{4}\right) + 3\right)$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module