Question

1+cos theta equal to

Answer 1

Cos(x+y) = Cosx. Cosy - Sinx. Siny (trigonometric function of the sum of 2 angles)

=> Cos( x+x) = Cosx Cosx - Sinx Sinx

=> Cos 2x = Cos²x - Sin²x

=> Cos 2x = Cos²x -(1-Cos²x) by identity cos²x+sin²x =1

=> Cos 2x = Cos²x -1 + Cos² x

=> Cos 2x = 2Cos² x -1

=> 1+ Cos 2x = 1+ 2Cos²x -1

=> 1 + Cos 2x = 2 Cos²x …………….…(1)

Now, if 2x = theeta, x = theeta/2

So, eq(1) => 1 + Cos theeta = 2 Cos² theeta

Answer 2

Answer:

Step-by-step explanation:

$cos(theta)= cos (theta/2 + theta/2)$

Replacing it into the question, we get:

1+ cos (theta/2 + theta/2)

Applying the formula of $cos(A+B)$, we get:

$1+ cos(thetha/2)^{2} - sin(theta/2)^{2}$

after re-arranging the driven formula, we get:

$2cos(theta/2)^{2}$