How? Which Trig Identityis that?

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The discussion revolves around identifying and correcting trigonometric identities related to a specific equation. The initial attempt at a solution incorrectly states the identity as sin^2 = 1 - cos^2, while the correct identity involves sin(2θ) and cos(2θ). The user ehild clarifies that the correct form of the equation should be 2000sin^2(500πt) = 1000(1 - cos(1000πt)). There is also a mention of a textbook error from Hambley's "Principles and Applications." The conversation highlights the importance of accurate trigonometric identities in solving equations.
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How?? Which Trig Identityis that?

Homework Statement






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The Attempt at a Solution


sin^2 = 1- cos^2 ??
 
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That looks wrong. It is close to the identity.

$$2\sin^2(x-\pi/4)=1-\sin(2x)$$
 
Yes. one of the relevant equation is sin2θ=1-cos2θ.
The other one is cos(2θ)=cos2θ-sin2θ. From these, you get the identity

sin2θ=.5(1-cos(2θ)). Use it.ehild
 
ehild said:
Yes. one of the relevant equation is sin2θ=1-cos2θ.
The other one is cos(2θ)=cos2θ-sin2θ. From these, you get the identity

sin2θ=.5(1-cos(2θ)). Use it.


ehild

but there is no sin..
 
k31453 said:
but there is no sin..

The equation you wrote in the first post is wrong. Correctly, it should be:

2000sin2(500πt)=1000(1-cos(1000πt)).

ehild
 
ehild said:
The equation you wrote in the first post is wrong. Correctly, it should be:

2000sin2(500πt)=1000(1-cos(1000πt)).

ehild

Awaks.. IT is solution of the Electrical Engineer : priniciples and application Hambley book.

And they made it wrong. I asked the question though i was wrong.
 

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