StudentChaitrali
  • StudentChaitrali
What is the max value of 4(sinx)^2+ 3(cosx)^2+ sin(x/2)+ cos(x/2)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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jim_thompson5910
  • jim_thompson5910
sin(x) maxes out at 1, so does cos(x)
jim_thompson5910
  • jim_thompson5910
\[\Large \sin(x) \le 1\] \[\Large \sin^2(x) \le 1^2\] \[\Large \sin^2(x) \le 1\] \[\Large 4*\sin^2(x) \le 4*1\] \[\Large 4\sin^2(x) \le 4\] hopefully this is making sense. If not, then let me know
IrishBoy123
  • IrishBoy123
this first bit simplifies straightaway ie by using Pythagoreas on \( 4\sin^2 x+ 3\cos^2 x\) you can combine these bits: \(\sin{x\over2}+ \cos{x\over2}\) as \(\sqrt{2} \{{ 1 \over \sqrt{2} } \sin{x\over2}+ { 1 \over \sqrt{2} } \cos{x\over2} \} = \sqrt{2} \sin ({x\over 2} + {\pi\over4})\) then maybe some calculus...after you have tidied it up. looks messy. personally, i'd stuff it in desmos.

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