Question

if tanAtanB=1 then cos(A+B)=?​

Answer 1

cos(A+B)= cosA cosB-SinAsinB

divide both sides by cosAcosB

cos(A+B)/cosAcosB=1-tanAtanB

cos(A+B)=cosAcosB(1-1)

cos(A+B)=0

Answer 2

Answer:

The answer to the given question is zero.

Step-by-step explanation:

Given :

tanAtanB=1

To find :

cos(A+B).

Solution :

As per the given data, the value of tanAtanB is given as 1 and we have to find the value of cos(A+B).

As we know the formula of cos(A+B) which is

cosAcosB-sinAsinB=cos(A+B).

let's divide both sides by CosACosB

$\frac{ \cos(A+B) }{ \cos( A) \cos(B) } = \frac{ \cos(A) \cos(B) - \sin(A) \sin(B) }{ \cos(A) \cos(B) }$

The above expression on the right-hand side can also be split as

$\frac{ \cos(A) \cos(B) }{ \cos(A) \cos(B) } - \frac{ \sin(A) \sin(B) }{ \cos(A) \cos(B) }$

The first term of the above expression will get cancelled.

As we know that

$\frac{ \sin}{ \cos} = \tan$

Therefore, the second term will become as tanAtanB

Then the above expression will become

$\frac{ \cos( A+ B) }{ \cos(A) \cos(B) } = 1 - \tan(A) \tan(B)$

The denominator on the left side becomes the multiplier on the right side.

$\cos( A+B ) = \cos(A) \cos(B) (1 - 1)$

as we know that the value of tanAtanB is given as 1.

$\cos( A+ B) = \cos(A) \cos(B) (0)$

anything multiplied by zero, the result will be zero.

Therefore, the final answer to the given question is zero.

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