Question

cos c + cos d is equal to​

Answer 1

Answer:

2cos(c+d/2)cos(c-d/2)❤

Answer 2

$cos\ c + cos\ d$ is equal to $2cos(\frac{c+d}{2} )cos(\frac{c-d}{2})$ .

Step 1 : Find the value.

Given - cos c + cos d = ?

Let c = a+b and d = a-b,

We can write it as,

$cos\ c+cos\ d = cos(a+b)+cos(a-b)$

$cos\ c+cos\ d = (cos\ a\ cos\ b-sin\ a\ sin\ b)+(cos\ a\ cos\ b+sin\ a\ sin\ b)\\\ cos\ c+cos\ d = cos\ a\ cos\ b-sin\ a\ sin\ b+cos\ a\ cos\ b+sin\ a\ sin\ b\\ cos\ c+cos\ d = 2cos\ a\ cos\ b$

As c = a+b and d = a-b,  So

$c+d=a+b+a-b\\c+d=2a\\\therefore a=\frac{c+d}{2}$

And

$c-d=a+b-(a-b)\\c-d=a+b-a+b\\c-d=2b\\\therefore b=\frac{c+d}{2}$

Substituting the value of 'a' and 'b' in the above equation,

$\therefore cos\ c + cos\ d = 2cos(\frac{c+d}{2} )cos(\frac{c-d}{2})$