In an acute angled ΔABC, the least value of sec A + sec B + sec C is:
6
Secant is strictly convex on \((0,\pi/2)\). Jensen’s inequality gives \(\sec A+\sec B+\sec C\ge3\sec((A+B+C)/3)=6\). Equality holds for an equilateral triangle.
Important Questions from Relations between AM, GM, HM
If \(a_1, a_2, a_3,...,a_n\) are positive real numbers whose product is a fixed number C, then the minimum value of \(a_1+a_2+...+a_n\) is
Let x be the HM and y be the GM of two positive numbers m and n. If 5x = 4y, then which one of the following is correct?
Consider the following statements:
1. cos θ + sec θ can never be equal to 1.5.
2. tan θ + cot θ can never be less than 2.
Which of the above statements is/are correct?Consider the following measures of central tendency for a set of N numbers:
1. Arithmetic mean.
2. Geometric mean.
Which of the above uses/use all the data?
The harmonic mean of two number is 4, Their arithmetic mean A and the geometric mean G satisfy the relation 2A + G 2= 27, then the two numbers are
