ข้อสอบ PAT 1 - มีนาคม 2557

ข้อ 11

กำหนดให้ theta เป็นจำนวนจริงใดๆ พิจารณาข้อความต่อไปนี้
left parenthesis ก right parenthesis space space 16 space sin cubed theta space cos squared theta space equals space 2 space sin space theta plus sin space 3 theta minus sin space 5 theta
left parenthesis ข right parenthesis space space sin space 3 theta space equals space open parentheses sin space 2 theta plus sin theta close parentheses open parentheses 2 space cos theta minus 1 close parentheses
ข้อใดต่อไปนี้ถูกต้อง

รีวิว - เสียงตอบรับจากผู้เรียน

เฉลยข้อสอบ

begin mathsize 12px style จากส ู ตร space thin space thin space thin space thin space thin space thin space thin space sin space A bond sinB equals 2 cos open parentheses fraction numerator A and B over denominator 2 end fraction close parentheses sin open parentheses fraction numerator A bond B over denominator 2 end fraction close parentheses
thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space cos space 2 A equals 1 minus sign 2 sin squared A
thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space sin space 3 A equals 3 sin space A minus sign 4 sin cubed A end style

begin mathsize 12px style left parenthesis italic ก right parenthesis space จากโจทย ์ space space 16 sin cubed italic theta space cos squared italic theta space equals space 2 sin space italic theta and sin space 3 italic theta minus sign sin space 5 italic theta

พ ิ จารณาฝ ั่ งขวา space equals 2 sin italic theta plus open parentheses sin space 3 italic theta minus sign sin 5 italic theta close parentheses
space space space space space space space space space space space space space space space space space space space space space space space space space space equals 2 sin italic theta and 2 cos left parenthesis fraction numerator 3 italic theta plus 5 italic theta over denominator 2 end fraction right parenthesis sin left parenthesis fraction numerator 3 italic theta minus sign 5 italic theta over denominator 2 end fraction right parenthesis
space space space space space space space space space space space space space space space space space space space space space space space space space space equals 2 sin italic theta and 2 cos 4 italic theta sin left parenthesis minus sign italic theta right parenthesis space end style
begin mathsize 12px style thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space bold โดย space open parentheses sin open parentheses negative theta close parentheses equals negative sin theta close parentheses
space space space space space space space space space space space space space space space space space space space space space space space space space space equals 2 sin theta minus 2 cos 4 theta sin theta
space space space space space space space space space space space space space space space space space space space space space space space space space space equals 2 sin theta open parentheses 1 minus cos 4 theta close parentheses rightwards arrow 2 sin theta open parentheses 1 minus cos 2 open parentheses 2 theta close parentheses close parentheses
space space space space space space space space space space space space space space space space space space space space space space space space space space equals 2 sin theta open parentheses 1 minus open parentheses 1 minus 2 sin squared space 2 theta close parentheses close parentheses
space space space space space space space space space space space space space space space space space space space space space space space space space space equals 2 sin theta times 2 sin squared space 2 theta rightwards arrow 2 sin theta times 2 open parentheses sin 2 theta close parentheses squared
space space space space space space space space space space space space space space space space space space space space space space space space space space equals 4 sin theta open parentheses 2 sin theta cos theta close parentheses squared
space space space space space space space space space space space space space space space space space space space space space space space space space space equals 16 sin cubed theta cos squared theta space space space space space space space space space space space space space space space space space space ข ้ อ space left parenthesis ก right parenthesis space ถ ู ก end style

begin mathsize 12px style left parenthesis ข right parenthesis space จากโจทย ์ space space sin 3 theta equals open parentheses sin 2 theta plus sin theta close parentheses open parentheses 2 cos theta minus 1 close parentheses

พ ิ จารณาฝ ั่ งขวา space equals open parentheses sin 2 theta plus sin theta close parentheses open parentheses 2 cos theta minus 1 close parentheses
space space space space space space space space space space space space space space space space space space space space space space space space space space equals open parentheses 2 sin theta cos theta plus sin theta close parentheses open parentheses 2 cos theta minus 1 close parentheses
space space space space space space space space space space space space space space space space space space space space space space space space space space equals sin theta open parentheses 2 cos theta plus 1 close parentheses open parentheses 2 cos theta minus 1 close parentheses
space space space space space space space space space space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space thin space thin space bold โดย space open parentheses a minus b close parentheses open parentheses a plus b close parentheses equals a squared minus b squared
space space space space space space space space space space space space space space space space space space space space space space space space space space equals sin theta open parentheses 4 cos squared theta minus 1 close parentheses
space space space space space space space space space space space space space space space space space space space space space space space space space space thin space thin space thin space thin space thin space thin space thin space bold โดย space sin squared theta plus cos squared theta equals 1 end style
                   begin mathsize 12px style equals sin theta open parentheses 4 open parentheses 1 minus sin squared theta close parentheses minus 1 close parentheses
equals sin theta open parentheses 4 minus 4 sin squared theta minus 1 close parentheses
equals sin theta open parentheses 3 minus 4 sin squared theta close parentheses
equals 3 sin theta minus 4 sin cubed theta
equals sin 3 theta space space space space space space space space space space space space space space space space space space ข ้ อ space left parenthesis ข right parenthesis space ถ ู ก end style

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