Find the value of cos 75
kashmir , 11 Years ago
Grade
Trigonometry> Find the value of cos 75...
2 AnswersRinkoo Gupta
cos75=cos(90-15)=sin15
sin^@=(1-cos(2@))/2
sin^15=(1-cos30)/2
=(1-(sqrt(3))/2)/2
=(2-sqrt3)/4
sin15=sqrt(2-sqrt3)/2
hence cos75=sqrt(2-sqrt3)/2 Ans.
Thanks & Regards
Rinkoo Gupta
AskIITians Faculty
Manas Satish Bedmutha
Simply using, cos 2A = 2 cos^2 A - 1
For A = 75, cos 150 = 2cos^2 75 - 1 = - cos 30
So, cos^2 75 = 1 - cos 30 = (2-sqrt3)/2x2
Hence, cos 75 = sqrt( (2-sqrt3) ) / 2
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