Grade 11Trigonometry

minimum value of cos(cosx) is what , with explanation

Rohit Roychoudhury

10 Years agoGrade 11

2 Answers

Jayakrishna Natarajan

Approved Tutor Answer10 Years ago

let y=cos(cosx)

dy/dx= sin(cosx)*sinx... dy/dx=0 @ x=2n(pi) or 2m+1(pi/2)

substituting this value for y..

y=cos1 or y=1

therefore range of y is [cos1,1]

jagdish singh singh

10 Years ago

$\hspace{-0.6 cm}$ Let $f(x)=\cos (\cos x)\;\forall x\in \mathbb{R}.$ Using $-1 \leq \cos x\leq 1$\\\\ So $ \cos 1 \leq \cos (\cos x)\leq 1.,$ Bcz $\cos x$ is an Decreasing function \\\\So above we have reverse Inequality and it is also an even function.\\\\So its value is same at two end points $\bf{i.e \; \cos(-1) = \cos (1)}$\\\\and Max. of $\cos$ is $\bf{1}.$ So $f(x)=\cos(\cos x)\in \left[\cos 1\;, 1\right].$$