How do you find the maximum value of 2cos(A+10)cos(A+20)? What is the value of A which makes it a maximum

Question

crashonce · Answer

@ganeshie8 
@ikram002p sorry if ur eating lol

ikram002p · Answer

hehe yeah lol , xD im late to breakfast brb

ganeshie8 · Answer

can we write it as below ?
$$\large  2\cos(A+10)\cos(A+20) = \cos(2A+30)  +  \cos(10)$$

crashonce · Answer

which identity?

ganeshie8 · Answer

2cosAcosB = cos(A+B) + cos(A-B)

crashonce · Answer

ohhhhhh ye ok

anonymous · Answer

a=30/2 ?

crashonce · Answer

i need steps @dg2  i dont care what the answer is, i need to learn

anonymous · Answer

idk i am asking....

ganeshie8 · Answer

rest should be easy to conclude as cos(10) is just a constant number

crashonce · Answer

ok but how do i find the max value

ganeshie8 · Answer

try below :

$$\large -1\le \cos(2A+30) \le  1$$

ganeshie8 · Answer

$$\large -1+\cos(10)\le \cos(2A+30) + \cos(10)\le  \color{purple}{1+\cos(10)}$$

ganeshie8 · Answer

that right side bound is the max value ^^

anonymous · Answer

a sin θ ± b cos θ =  ±√ (a2 + b2 ) { for min. use – , for max. use + }

anonymous · Answer

when we are using this formulae idk?

aum · Answer

The question asks for the value of A that will make the expression a maximum.

crashonce · Answer

thanks guise

ganeshie8 · Answer

np :) again, the question is also asking about what value(s) of A makes it maximum...

ganeshie8 · Answer

you still need to solve :  $   \cos(2A+30) = 1$ for A values that give u max

crashonce · Answer

ty

anonymous · Answer

this problem is over ahh?

anonymous · Answer

A plot and solution using Mathematica v9 is attached.