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If cos(θ - α) = 3/5 and sin(θ - α) = 12/13, then the value of cos 2α  may be: A....

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nasirjam | Student, Grade 9 | Honors

Posted December 16, 2012 at 9:55 AM via web

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If cos(θ - α) = 3/5 and sin(θ - α) = 12/13, then the value of cos 2α  may be:

A. 32/65

B. 63/65

C. 48/65

D. 34/65

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lfryerda | High School Teacher | (Level 2) Educator

Posted December 16, 2012 at 4:03 PM (Answer #1)

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This question is ill-formed, which means that it is inconsistent with trigonometry.  If it was properly formed, then we know that for any angle, `sin^2x+cos^2x=1` , even if the angle is `x=theta-a` .

However, this means that 

`cos^2(theta-a)=9/25`

and 

`sin^2(theta-a)=144/169`  and they should add to 1.

But:

`9/25+144/169 = 5121/4225 ne 1`

This question has no solution.

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