Question

prove that cos 60° = cos²30°- sin²30°​

Answer 1

Hey There

Here's The Answer

__________________________

• To Prove : cos 60° = cos²30° - sin²30°

• R.H.S.

=> cos² 30° - sin² 30°

=> ( √3 / 2 )² - ( 1 / 2 )²

=> 3/4 - 1/4

=> ( 3 - 1 )/4

=> 2/4

=> 1/2

• L.H.S.

=> cos 60°

=> 1/2

• Hence, L.H.S. = R.H.S. = 1/2

Hope It Helps.

Answer 2

cos60=1/2—————- 1
Now
cos^2 30 =(root 3/2)^2=3/4
sin^2 30 =(1/2)^2=1/4
cos^2 30- sin^2 30= (3/4)-(1/4)
=2/4=1/2 ——————- 2
From 1 and 2
cos 60=cos^2 30-sin^2 30