Cos 22.5

Since #22.5^@ = 1/2xx45^@# we will want to use the half angle formula for #cos# #cos(theta/2) = +-sqrt((1+cos(theta))/2)# #color(white)("XXX")#(we will ignore the negative version since for this example our angle falls in Quadrant I where #cos# is positive) #cos(22.5^@) = sqrt((1+cos(45^@))/2)# #color(white)("XXXXXX")=sqrt((1+1/sqrt(2))/2)# #color(white)("XXXXXX")=sqrt(2+sqrt(2))/2# (using a calculator) #color(white)("XXXXXX")~=0.92388#

• \cos(45^) • 4-2\arctan(4) Frequently Asked Questions (FAQ) • What is the value of cos^2(22.5)-sin^2(22.5) ? • The value of cos^2(22.5)-sin^2(22.5) is (sqrt(2))/2 •

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• Course • NCERT • Class 12 • Class 11 • Class 10 • Class 9 • Class 8 • Class 7 • Class 6 • IIT JEE • Exam • JEE MAINS • JEE ADVANCED • X BOARDS • XII BOARDS • NEET • Neet Previous Year (Year Wise) • Physics Previous Year • Chemistry Previous Year • Biology Previous Year • Neet All Sample Papers • Sample Papers Biology • Sample Papers Physics • Sample Papers Chemistry • Download PDF's • Class 12 • Class 11 • Class 10 • Class 9 • Class 8 • Class 7 • Class 6 • Exam Corner • Online Class • Quiz • Ask Doubt on Whatsapp • Search Doubtnut • English Dictionary • Toppers Talk • Blog • Download • Get App Doubtnut is No.1 Study App and Learning App with Instant Video Solutions for NCERT Class 6, Class 7, Class 8, Class 9, Class 10, Class 11 and Class 12, IIT JEE prep, NEET preparation and CBSE, UP Board, Bihar Board, Rajasthan Board, MP Board, Telangana Board etc NCERT solutions for CBSE and other state boards is a key requirement for students. Doubtnut helps with homework, doubts and solutions to all the questions. It has helped students get under AIR 100 in NEET & IIT JEE. Get PDF and video solutions of IIT-JEE Mains & Advanced previous year papers, NEET previous year papers, NCERT books for classes 6 to 12, CBSE, Pathfinder Publications, RD Sharma, RS Aggarwal, Manohar Ray, Cengage books for boards and competitive exams. Doubtnut is the perfect NEET and IIT JEE preparation App. Get solutions for NEET and IIT JEE previous years papers, along with chapter wise NEET MCQ solutions. G...

Since #22.5^@ = 1/2xx45^@# we will want to use the half angle formula for #cos# #cos(theta/2) = +-sqrt((1+cos(theta))/2)# #color(white)("XXX")#(we will ignore the negative version since for this example our angle falls in Quadrant I where #cos# is positive) #cos(22.5^@) = sqrt((1+cos(45^@))/2)# #color(white)("XXXXXX")=sqrt((1+1/sqrt(2))/2)# #color(white)("XXXXXX")=sqrt(2+sqrt(2))/2# (using a calculator) #color(white)("XXXXXX")~=0.92388#