Question

sin a+sin b=2 find the value of cos a - cos b​

Answer 1

$\bold{Answer:}$

The maximum value of the sine of an angle is 1 and this is the sine of 90 degrees only. So, if the sum of the sines of two angles total 2, the value of each angle must be 90 degrees. The sine of any angle which is not 90 degrees is less than 1.

With this knowledge, it is evident that both angles A and B must be 90 degrees, i.e., angle A = angle B.

Knowing that both angles A and B are 90 degrees and that the value of the cosine of 90 degrees is 0 (zero), we can deduce that cosA = 0 and that cosB = 0 also.

Hence: cosA + cos B = 0 + 0 = 0.

ANSWER: cosA + cos B = 0. QED.

Answer 2

Answer:

Step-by-step explanation:

Since -1<=Sin A<=1 and -1<=Sin B<=1 for A, B € R;

Hence -2 <=Sin A + Sin B <=2 ;

But according to question Sin A + Sin B = 2 ;

So Sin A = 1 and Sin B = 1 ;

So A = B = 2 * n *π + (π/2) ; where n€ Z;

So both Cos A and Cos B both takes values zero so their sum ie. Cos A + Cos B = 0 .