Proving Identities: Cos^2(x)= (1+Cos2x)/2

  • Thread starter Thread starter banfill_89
  • Start date Start date
  • Tags Tags
    identities
Click For Summary
To prove the identity cos^2(x) = (1 + cos(2x))/2, the right-hand side is simplified using the double angle formula. By substituting cos(2x) with 2cos^2(x) - 1, the expression becomes (1 + (2cos^2(x) - 1))/2. This simplifies to cos^2(x), confirming the identity. The solution is validated and deemed correct. The proof effectively demonstrates the equivalence of both sides.
banfill_89
Messages
47
Reaction score
0

Homework Statement


prove: cos^2(x)= (1+cos2x)/(2)


Homework Equations


i broke the cos^2(x) down to 1-sin^2(x)?


The Attempt at a Solution

 
Physics news on Phys.org
It's easier to start with the right hand side. Just apply the double angle formula on the right.
 
this is what i did:

= (1+cos2x)/(2)
= (1+ (2cos^2(x)-1))/(2)
= 2cos^2 (x)/2
cos^2(x)=cos^2(x)

look good?
 
Yeah looks ok.
 
awsome thanksman
 

Thread 'Distance between a Clock's hands when the distance is increasing most rapidly'

Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?
View full post »

Similar threads

lim x-->0 ##\frac{x tan2x -2xtanx} {(1-cos2x)^2}##
  • · Replies 5 ·
Replies
5
Views
1K
Integration of even powers of sine and cosine
  • · Replies 2 ·
Replies
2
Views
3K
Calculating radius of gyration of plane figure about x-axis
  • · Replies 5 ·
Replies
5
Views
2K
Integrate: cos2x/[cos^2 (x).sin^2 (x)]-cot(x)/2
  • · Replies 4 ·
Replies
4
Views
2K
Proving trigonometry identities
  • · Replies 4 ·
Replies
4
Views
1K
Finding the Sine Representation of an Odd Function Using Fourier Series
  • · Replies 12 ·
Replies
12
Views
6K
What is the Fundamental Period of a Function with a Given Derivative?
  • · Replies 6 ·
Replies
6
Views
1K
How do we write a sinusoidal solution to a 2nd order DE as a sum of exponentials raised to complex roots?
  • · Replies 2 ·
Replies
2
Views
2K
Integrating cos^2x with the Chain Rule: Explanation and Example
  • · Replies 4 ·
Replies
4
Views
5K
##\lim_{x \to0} \left(\dfrac{1}{\sin^2 x}-\dfrac{1}{x^2}\right)##
  • · Replies 5 ·
Replies
5
Views
2K