Home
Class 12
MATHS
If A+B+C=pi , prove that cotA+cotB+cotC-...

If `A+B+C=pi` , prove that `cotA+cotB+cotC-cos e cAdotcos e cBdotcos e cC=cotAdotcotBdotcotCdot`

Text Solution

Verified by Experts

(a) `A+B+C=(pi//2)rArrA+B=(pi//2)-C`
`rArr tan(A+B)=tan(pi//2-C)`
`rArr (tan A+tanB)/(1-tanA tan B)=cotC`
Now convert all the terms cot and simplify.
(b) Replace `cot C` by `(1)/(tanC)` in Eq. i and simplify.
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise 3.9|5 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise 3.10|5 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise 3.7|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

In A B C , prove that cos e c A/2+cos e c B/2+cos e c C/2geq6.

If A+B+C=pi prove that cos^(2) A+cos^(2) B+cos^(2) C=1 - 2cos A cos B cos C .

In A B C , if cotA+cotB+cotC=0 then find the value of cosAcos BcosC

The value of cos e c10^0+cos e c50^0-cos e c70^0 is ____

Find the sum of the series cos e ctheta+cos e c2theta+cos e c4theta+ tont e r m sdot

In a triangle ABC, if sinAsin(B-C)=sinCsin(A-B), then prove that cotA ,cotB ,cotC are in AdotPdot

In any /_\ A B C , prove that (b^2-c^2)cotA+(c^2-a^2)cotB+(c^a-b^2)cotC=0

If cos e cA+secA=cos e c B+s e cB , prove that: "tanAtanB"=cot(A+B)/2

Which of the following is the greates? cos e c1 (b) cos e c2 cos e c4 (d) cos e c(-6)

If A , B , C , D are the angles of a quadrilateral, then (tanA+tanB+tanC+tanD)/(cotA+cotB+cotC+cotD)i se q u a lto: tanAtanBtanCtanD cotAcotBcotCcotD tan^2A+tan^2B+tan^2C+tan^2D sumtanAtanBtanC