Home
Class 12
MATHS
In acute angled triangle ABC prove that ...

In acute angled `triangle ABC` prove that `tan ^(2)A+tan^(2)B+tan^(2)Cge9`.

Text Solution

Verified by Experts

we know that in acute angled triangle ABC,
`tan A tan B tan Cge3sqrt(3)`.
`(tan^(2)A+tan^(2)B+tan^(2)C)/(3)ge(tan^(2)A.tan^(2)B.tan^(2)C)^(1//3)`
`therefore tan^(2)A+tan^(2)B+tan^(2)Cge3(27)^(1//3)`
`rArr tan^(2)A+tan^(2)B+tan^(2)Cge9`.
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise (Single)|100 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise (Multiple)|22 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise 3.9|5 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

  • TRIGONOMETRIC RATIOS FOR COMPOUND, MULTIPLE, SUB-MULTIPLE ANGLES, AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Multiple Correct Answers Type|6 Videos

Similar Questions

Explore conceptually related problems

Prove that tan2A =(2tanA)/(1-tan^2 A)

If A+B+C=pi, prove that tan^2A/2+tan^2B/2+tan^2C/2geq1.

Prove that tan70^0=2tan50^0+tan20^0

In triangle ABC, prove that the maximum value of tan(A/2)tan(B/2)tan(C/2)i s R/(2s)

In any triangle A B C , prove that following : c/(a+b)=(1-tan(A/2)tan(B/2))/(1+tan(A/2)tan(B/2))

Prove that cos2A=(1-tan^2 A)/(1+tan^2 A)

If A , B and C are interior angles of a triangle ABC, then show that tan ((A+B) /(2)) =cot ©/(2)

If cos theta=a/(b+c), cos phi= b/(a+c) and cos psi=c/(a+b) where theta, phi, psi in (0, pi) and a,b,c are sides of triangle ABC then tan^2(theta/2)+tan^2(phi/2)+tan^2(psi/2)=

The value of tan^2 A - tan^2 B is

Prove that tan3A=(3tanA-tan^3 A)/(1-3tan^2 A)