Prove that: cos pi/12-sin pi/12=1/root 2.What should be the answer for this question?

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Answer 1 · 2018-04-20T10:17:34

Please refer to a Proof in the Explanation.

We have, $cos(pi/12)-sin(pi/12)$ ,

$=sqrt2{1/sqrt2*cos(pi/12)-1/sqrt2*sin(pi/12)}$ ,

$=sqrt2{cos(pi/4)cos(pi/12)-sin(pi/4)sin(pi/12)}$ ,

$=sqrt2cos(pi/4+pi/12)$ ,

$=sqrt2cos((4pi)/12)=sqrt2cos(pi/3)$ ,

$=sqrt2*1/2$ .

$rArr cos(pi/12)-sin(pi/12)=1/sqrt2$ .

Answer 2 · 2018-04-20T10:19:35

See below.

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Do you understand this method?