Can you find the trick behind it
Level
pending
Range of f(x) = Cosx (Sinx +√((Sinx)^2 +0.5)) is [-√y, √z] then find y+z.
The answer is 3.
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1 solution
Range of aSinx+bCosx is [-√(a^2+b^2),√(a^2+b^2)] Multiply cosx inside, then it will be Sinx Cosx+ Cosx [√((Sinx)^2+0.5)] Let Sinx=a and [√((Sinx)^2+0.5)]=b therefore a^2+b^2 = (Cosx)^2+(Sinx)^2+0.5=1.5 . Then y=z=1.5 so y+z=3. So, answer is 3