Home
Class 12
MATHS
Find the least value of secA+secB+secC i...

Find the least value of `secA+secB+secC` in an acute angled triangle.

Text Solution

Verified by Experts

Triangle ABC is acute angled
`therefore 0 ltA,B,C lt pi//2`
so , consdier the graph of function `y = sec x for x in (0,pi//2)`
The graph of funtion is concave upward
`therefore (secA+secB+secC)/(3)gesec(A+B+C)/(3)`
`rarr (secA+secB+secC)/(3)gesec(pi)/(3)`
`rarr secA+secB+secCge6`
Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise Exercise 6.4|16 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise Exercise 6.5|5 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise Exercise 6.2|10 Videos

  • METHODS OF DIFFERETIATION

    CENGAGE|Exercise Question Bank|29 Videos

  • MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS

    CENGAGE|Exercise Comprehension Type|6 Videos

Similar Questions

Explore conceptually related problems

Find the least value of sec A+sec B+sec C in an acute angled triangle

The minimum value of tan B tan C in an acute angled triangle ABC is

Find the value of (tanA+secA-1)cosA .

Naming triangles by considering the measures of their angles acute triangle A triangle whose all the angles are acute is called an acute- angled triangle or an acute triangle.

For a /_\ABC, if cotA.cotB.cotCgt0 , then nature of the triangle is (A) acute angled triangle (B) right angled triangle (C) obtuse angled triangle (D) none of these

Prove that in an acute triangle ABC,the least values of Sigma sec A and Sigma tan^(2)A are 6 and 9 respectively.