PR math sat ii question

Test Preparation SAT Subject Test Preparation
1

<p>Hello. I have a problem (an example problem) from the Princeton Review Math sat ii book.
If A represents an angle such that sin2A=tanA - cos2A, then sinA-cosA=
a) -sqr(2)
b) 0
c) 1
d) 2 * sqr(2)
e)it cannot be determined </p>

<p>(PS: sqr means square root). </p>

<p>by the way this question is on page 17, number 49 from the newest PR Maths sat subject test book.
thanks in advance!!!</p>

2

<p>The question implies that it requires the use of double-angle identities, but I was unable to get anywhere with manipulating the formula.</p>

<p>Can you double check that you wrote the question correctly?</p>

3

<p>I started thinking of the possible special values that made the equation true until I can to pi/4. Pi/4 works and so the answer is 0 bc sin pi/4 - cos pi/4=0</p>

4

<p>A full solution can be found here, post #8:
<a href=“http://talk.collegeconfidential.com/sat-subject-tests-preparation/1547837-how-hell-can-one-memorize-all-trig-formulas-math-iic.html[/url]”>http://talk.collegeconfidential.com/sat-subject-tests-preparation/1547837-how-hell-can-one-memorize-all-trig-formulas-math-iic.html&lt;/a&gt;&lt;/p&gt;

<p>My solution basically involved using some double-angle formulae to show that the original equation was equivalent to</p>

<p>(cos A - sin A)(sin 2A + 1) = 0</p>

<p>Hence cos A - sin A = 0 (choice B, e.g. let A = pi/4) or A = 3pi/4. Since these give different results for sin A - cos A, the correct answer is E) It cannot be determined.</p>