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elizabeth
12-28-2013, 04:41 PM
Trigonometry double angle formula SAT Subject test Math level 2

Which of the following is the value of \frac{5}{cos^22x- sin^22x } given that cos4x=\frac{1}{2}?

(A) 5
(B) \frac{1}{2}
(C) \frac{5}{2}
(D) \frac{5}{4}
(E) 10

Thanks!:o

Oliver
12-28-2013, 04:42 PM
The double angle formula is given by
cos2x= cos^2x- sin^2x=1-2sin^2x=2cos^2x-1

So, cos^22x- sin^22x = cos2(2x)=cos4x=\frac{1}{2} .

Finally the required value is \frac{5}{cos^22x- sin^22x }=\frac{5}{\frac{1}{2}}=10

Therefore the correct answer is (E).

elizabeth
12-28-2013, 04:42 PM
Thank you!