Double angle identities question

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Monkeyseat

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Jul 3, 2005
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298
Question:

Given that cos (2A) = tan^2 (x), show that cos (2x) = tan^2 (A).

Working:

Sorry, I'm stumped with this. I don't even know how to start it. Any tips would be greatly appreciated.

Many thanks.
 
Monkeyseat said:
Question:

Given that cos (2A) = tan^2 (x), show that cos (2x) = tan^2 (A).

Hint:
cos (2A) = tan[sup:1ohchao9]2[/sup:1ohchao9](x)

2cos[sup:1ohchao9]2[/sup:1ohchao9](A) - 1 = sec[sup:1ohchao9]2[/sup:1ohchao9](x) - 1

Working:

Sorry, I'm stumped with this. I don't even know how to start it. Any tips would be greatly appreciated.

Many thanks.
Click to expand...
 
Thank you very much.

Okay, I think I may have done it.

cos (2A) = tan[sup:26xk2233]2[/sup:26xk2233](x)
2cos[sup:26xk2233]2[/sup:26xk2233](A) - 1 = sec[sup:26xk2233]2[/sup:26xk2233](x) - 1
2cos[sup:26xk2233]2[/sup:26xk2233](A) = sec[sup:26xk2233]2[/sup:26xk2233](x)
2cos[sup:26xk2233]2[/sup:26xk2233](A) = 1/(cos[sup:26xk2233]2[/sup:26xk2233](x))
2cos[sup:26xk2233]2[/sup:26xk2233](A) cos[sup:26xk2233]2[/sup:26xk2233] (x) = 1
2cos[sup:26xk2233]2[/sup:26xk2233](x) = 1/(cos[sup:26xk2233]2[/sup:26xk2233](A))
2cos[sup:26xk2233]2[/sup:26xk2233](x) = sec[sup:26xk2233]2[/sup:26xk2233](A)
cos (2x) + 1 = sec[sup:26xk2233]2[/sup:26xk2233](A)
cos (2x) = sec[sup:26xk2233]2[/sup:26xk2233](A) - 1
cos (2x) = tan[sup:26xk2233]2[/sup:26xk2233](A)

Is that ok? Thanks.
 
Monkeyseat said:
Thank you very much.

Okay, I think I may have done it.

cos (2A) = tan[sup:3isdn475]2[/sup:3isdn475](x)
2cos[sup:3isdn475]2[/sup:3isdn475](A) - 1 = sec[sup:3isdn475]2[/sup:3isdn475](x) - 1
2cos[sup:3isdn475]2[/sup:3isdn475](A) = sec[sup:3isdn475]2[/sup:3isdn475](x)
2cos[sup:3isdn475]2[/sup:3isdn475](A) = 1/(cos[sup:3isdn475]2[/sup:3isdn475](x))
2cos[sup:3isdn475]2[/sup:3isdn475](A) cos[sup:3isdn475]2[/sup:3isdn475] (x) = 1
2cos[sup:3isdn475]2[/sup:3isdn475](x) = 1/(cos[sup:3isdn475]2[/sup:3isdn475](A))
2cos[sup:3isdn475]2[/sup:3isdn475](x) = sec[sup:3isdn475]2[/sup:3isdn475](A)
cos (2x) + 1 = sec[sup:3isdn475]2[/sup:3isdn475](A)
cos (2x) = sec[sup:3isdn475]2[/sup:3isdn475](A) - 1
cos (2x) = tan[sup:3isdn475]2[/sup:3isdn475](A) <<<< Correct

Is that ok? Thanks.
Click to expand...
 
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