Question

1+cosx = 2cos square x/2 prove the statement!! step by step

Answer 1

cos x = cos ( x/2 + x/2)
now by the rule of multiple angles
cos (A+B ) = cosAcosB -sinAsinB
so cos x = cos( x/2 + x/2)
= cos squared x/2 - sin squared x/2 .......(1)
Now we know sin squared α+ cos squared α = 1 so,
sin squared x/2 + cos squared x/2 = 1
=> sin squared x/2 = 1 - cos squared x/2 .....(2)
Putting the value of (2) in (1) we get
cos x = cos squared x/2 - ( 1 - cos squared x/2)
=> cos x = 2cos squared x/2 - 1
=> 1 + cos x = 2cos squared x/2