(bsecB+csecC)/(tanB+t a n C)=(csecC+asec...

`(bsecB+csecC)/(tanB+t a n C)=(csecC+asecA)/(tanC+t a n A)=(asecA+bsecB)/(tanA+t a n B)dot`

Text Solution

Verified by Experts

Let a, b, c be the sides of any triangle ABC. Then by applying the sine rule, we get
`a/sinA=b/sinB=c/sinC=k`
`a=k sin A,b=ksinB,c=k sinC`
L.H.S=`(bsecB+csecC)/(tanB+t a n C)`
=`(b/cos B+c/cos C)/(sinB/cos B+sinC/cos C)[since secA=1/cos A and tanC=sin C/cos C]`
=`[(b cos C+c cos B)/(cos B cos C)]/[(sin B cos C+sin C cos B)/(cos C cos B)]`
=`(b cos C+c cos B)/(sin B cos C+sin C cos B)`
Substituting values from sine law, we get
...

Topper's Solved these Questions

SETS
RD SHARMA|Exercise Solved Examples And Exercises|218 Videos
SOME SPECIAL SERIES
RD SHARMA|Exercise Solved Examples And Exercises|69 Videos

Similar Questions

Explore conceptually related problems

If A+B+C=180^0 , then (t a n A+t a n B+t a n C)/(t a n A t a n B t a n C) is equal to t a n A t a n B t a n C b. 0 c. 1 d. none of these

Statement 1 is True: Statement 2 is True; Statement 2 is a correct explanation for statement 1 Statement 1 is true, Statement 2 is true;2 Statement 2 not a correct explanation for statement 1. Statement 1 is true, statement 2 is false Statement 1 is false, statement 2 is true Statement I: If A is obtuse angle I A B C , then tanB\ t a n C<1 because Statement II: In A B C ,\ t a n A=(t a n B+t a n C)/(t a n B t a n C-1)\ a. A b. \ B c. \ C d. D

If A+B+C=pi , prove that : (cotA+cotB)/(tanA+tanB) + (cotB+cotC)/(tanB+tanC) + (cotC+cotA)/(tanC+tanA) =1

If A , B , C are in A.P. then (sin A-sin C)/(cos C-cos A)= adot t a n B b. cot B c. t a n2B d. none of these

If A + B + C = π , Prove that tanB tanC+tanC tanA+tanA tanB=1+secA . sec B . secC.

If A+B+C=180^(@) , then (tanA+tanB+tanC)/(tanAtanBtanC)=?

If cos(A+B)sin(C-D)="cos"(A-B)"sin"(C+D) , then write the value of t a n A t a n B t a n Cdot

If A+B+C=pi , prove that : (tanA+tanB+tanC) (cotA+cotB+cotC)=1+secA secB secC .

In triangle A B C ,tanA+tanB+tanC=6a n dtanAtanB=2, then the values of tanA ,tanB ,tanC are, respectively (a)1,2,3 (b) 3,2//3,7//3 (c)4,1//2 ,3//2 (d) none of these

The growth of a quantity N (t) at any constant t is given by (d N (t))/(dt) = alpha N (t) . Given that N (t) = ce^(kt) .c is a constant . What is the value of alpha ?

RD SHARMA-SINE AND COSINE FORMULAE AND THEIR APPLICATIONS-Solved Examples And Exercises

(sqrt(sinA)-sqrt(sinB))/(sqrt(sinA)+sqrt(sinB)) = (a+b-2sqrt(ab))/(a-b...
Text Solution
|
The angle of elevation of the top of a tower from a point A due south ...
Text Solution
|
(bsecB+csecC)/(tanB+t a n C)=(csecC+asecA)/(tanC+t a n A)=(asecA+bsecB...
Text Solution
|
a(cosC-cosB)=2(b-c)cos^2A/2
Text Solution
|
a^2(cos^2B-cos^2C)+b^2(cos^2C-cos^2A)+c^2(cos^2A-cos^2B)=0 .
Text Solution
|
cos(2A)/a^2-cos(2B)/b^2 = 1/a^2-1/b^2
Text Solution
|
In a Delta A B C ,\ if\ a=2,\ b=3\ a n d\ sin A=2/3 then find /B
Text Solution
|
In any triangle A B C , prove that: (sin(B-C))/(sin(B+C))=(b^2-c^2)/(a...
Text Solution
|
In any triangle A B C , prove that: \ asin(B-C)+b s in(C-A)+csin(A-B)=...
Text Solution
|
In any triangle A B C , prove that: \ a^3sin(B-C)+b^3sin(C-A)+c^3sin(A...
Text Solution
|
In any triangle A B C prove that: sin((B-C)/2)=((b-c)/a)cosA/2
Text Solution
|
In any triangle A B C , prove that: (b-c)/(b+c)=(tan((B-C)/2))/(tan((B...
Text Solution
|
In any triangle A B C , prove that: acos((B+C)/2)=(b+c)sinA/2
Text Solution
|
A tree stands vertically on a hill side which makes an angle of 15^0 w...
Text Solution
|
A person, standing on the bank of a river, observes that the angle sub...
Text Solution
|
The angle of elevation of to be top point P of the vertical tower PQ o...
Text Solution
|
The elevation of a tower at a station A due North of it is alpha and ...
Text Solution
|
If in a Delta A B C ,\ /A=45^0,\ /B=60^0,\ a n d\ /C=75^0 , find the ...
Text Solution
|
If in any Delta A B C ,\ /C=105^0,/B=45^0, a=2, then find bdot
Text Solution
|
In Delta A B C ,\ if\ a=18 ,\ b=24\ a n d\ c=30\ a n d\ /C=90^0 find ...
Text Solution
|