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Question Number 129360 by bramlexs22 last updated on 15/Jan/21
{sina+sinb=13cosa+cosb=53cos2(a+b)=?
Commented by bramlexs22 last updated on 15/Jan/21
nicetrigonometry
Answered by liberty last updated on 15/Jan/21
(1)cos(a−b)=49(2)sin(a+b)+sin(a+b)cos(a−b)=59⇒sin(a+b)+49sin(a+b)=59⇒139sin(a+b)=59⇒sin(a+b)=513⇒cos2(a+b)=1−25169=144169
Answered by bramlexs22 last updated on 15/Jan/21
⇔2sin(a+b2)cos(a−b2)2cos(a+b2)cos(a−b2)=15⇔tan(a+b2)=15⇒tan(a+b)=2tan(a+b2)1−tan2(a+b2)⇒tan(a+b)=251−125=1024=512⇒sec2(a+b)=1+25144=169144⇒cos2(a+b)=144169
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