Home
Class 12
MATHS
Minimum value of (sec^4alpha)/(tan^2beta...

Minimum value of `(sec^4alpha)/(tan^2beta)+(sec^4beta)/(tan^2alpha),` where `alpha!=pi/2,beta!=pi/2,0

Text Solution

Verified by Experts

The correct Answer is:
8
Let `a =tan^2alpha,b-tan^2beta`
Given expression becomes
`((a+1)^2)/b+((b+1)^2)/a (age,bge0)`
`=(a^2+2a+1)/b+(b^2+2b+1)/a`
`=a^2/b+1/b+b^2/a+1/a+2(a/b+b/a)`
`ge4.4sqrt(a^2/b. 1/b b^2/(a.a))+2(2)`
`=4+4=8`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise JEE Main Previous Year|2 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise JEE Advanced Previous Year|2 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise (Matrix)|3 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Archives (Matrix Match Type)|1 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Matrix Match Type|1 Videos

Similar Questions

Explore conceptually related problems

Minimum value of (sec^(4)alpha)/(tan^(2)beta)+(sec^(4)beta)/(tan^(2)alpha), where alpha!=(pi)/(2),beta!=(pi)/(2),0

Prove that (sec^4alpha)/(tan^2beta)+(sec^4beta)/(tan^2alpha)ge8 . If each term in the expression is well defined.

If (sec^(4)alpha)/(sec^(2)beta)-(tan^(4)alpha)/(tan^(2)beta)=1 where alpha,betane(pi)/(2) , then find the value of (sec^(4)beta)/(sec^(2)alpha)-(tan^(4)beta)/(tan^(2)alpha)

If x sec alpha+y tan alpha=x sec beta+y tan beta=a , then sec alpha*sec beta=

The value of tan^(2)alpha-tan^(2)beta-(1)/(2)sin(alpha-beta)sec^(2)alpha sec^(2)beta is zero if

Maximum value of sin alpha+sin beta+2, where alpha +beta =120^(^^)@ alpha,beta in (0,pi/2)

If sec alpha is the average of sec(alpha-2 beta) and sec(alpha+2 beta) then the value of (2sin^(2)beta-sin^(2)alpha) where beta!=n pi is

[ 7.If 0ltalphaltbetalt(pi)/(2) then [ 1) (tan beta)/(tan alpha)lt(alpha)/(beta), 2) (tan beta)/(tan alpha)gt(alpha)/(beta) 3) (tan alpha)/(tan beta)lt(alpha)/(beta) , 4) none ]]

If alpha and beta are the roots of the equation x^(2)-4x+1=0(alpha

If alpha+beta=(pi)/(2) and beta+gamma=alpha then tan alpha=