## StudentChaitrali one year ago What is the max value of 4(sinx)^2+ 3(cosx)^2+ sin(x/2)+ cos(x/2)

1. jim_thompson5910

sin(x) maxes out at 1, so does cos(x)

2. 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

3. 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.