# 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 | Certified Educator

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.**