Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

In $capital delta A B C comma a squared c o t invisible function application A plus b squared c o t invisible function application B plus C squared c o t invisible function application C equals$

$Δ$
2 $Δ$
3 $Δ$
4 $Δ$

hint Hint:

In this question we have to use Sine rule
$a space equals 2 R sin open parentheses A close parentheses b equals 2 R sin open parentheses B close parentheses c equals 2 R sin open parentheses C close parentheses$
then we will use trigonometric formula $sin open parentheses A close parentheses plus sin open parentheses B close parentheses equals space 2 sin open parentheses fraction numerator A plus B over denominator 2 end fraction close parentheses cos open parentheses fraction numerator A minus B over denominator 2 end fraction close parentheses$ and $cos open parentheses A plus B close parentheses plus cos open parentheses A minus B close parentheses equals space 2 sin open parentheses A close parentheses sin open parentheses B close parentheses$ . Then at last we will use $fraction numerator a b c over denominator R end fraction equals 4 increment$ .

The correct answer is: 4 $capital delta$

$sin open parentheses 2 x close parentheses equals 2 sin open parentheses x close parentheses cos open parentheses x close parentheses$ In this question we have to find the value of $a squared cot open parentheses A close parentheses plus b squared cot open parentheses B close parentheses plus c squared cot open parentheses C close parentheses$
By using Sine Rule
$a space equals 2 R sin open parentheses A close parentheses b equals 2 R sin open parentheses B close parentheses c equals 2 R sin open parentheses C close parentheses$
by substituting these value in the given expression
=> $left parenthesis 2 R sin open parentheses A close parentheses right parenthesis squared cot open parentheses A close parentheses plus left parenthesis 2 R sin open parentheses B close parentheses right parenthesis squared cot open parentheses B close parentheses plus left parenthesis 2 R sin open parentheses C close parentheses right parenthesis squared cot open parentheses C close parentheses$
=> $4 R squared left parenthesis sin squared open parentheses A close parentheses cot open parentheses A close parentheses plus sin squared open parentheses B close parentheses cot open parentheses B close parentheses plus sin squared open parentheses C close parentheses cot open parentheses C close parentheses right parenthesis$
We know that $cot open parentheses x close parentheses equals fraction numerator cos open parentheses x close parentheses over denominator sin open parentheses x close parentheses end fraction$ and
=> $4 R squared left parenthesis sin open parentheses A close parentheses cos open parentheses A close parentheses plus sin open parentheses B close parentheses cos open parentheses B close parentheses plus sin open parentheses C close parentheses cos open parentheses C close parentheses right parenthesis$
=> $2 R squared left parenthesis 2 sin open parentheses A close parentheses cos open parentheses A close parentheses plus 2 sin open parentheses B close parentheses cos open parentheses B close parentheses plus 2 sin open parentheses C close parentheses cos open parentheses C close parentheses right parenthesis$
=> $2 R squared left parenthesis sin open parentheses 2 A close parentheses plus sin open parentheses 2 B close parentheses plus sin open parentheses 2 C close parentheses right parenthesis$
We know that $sin open parentheses A close parentheses plus sin open parentheses B close parentheses equals space 2 sin open parentheses fraction numerator A plus B over denominator 2 end fraction close parentheses cos open parentheses fraction numerator A minus B over denominator 2 end fraction close parentheses$
=> $2 R squared left parenthesis 2 sin open parentheses A plus B close parentheses cos open parentheses A minus B close parentheses plus 2 sin open parentheses C close parentheses cos open parentheses C close parentheses right parenthesis$
=> $A plus B equals pi minus C$
=> $2 R squared left parenthesis 2 sin open parentheses pi minus C close parentheses cos open parentheses A minus B close parentheses plus 2 sin open parentheses C close parentheses cos open parentheses C close parentheses right parenthesis$
=> $2 R squared left parenthesis 2 sin open parentheses C close parentheses cos open parentheses A minus B close parentheses plus 2 sin open parentheses C close parentheses cos open parentheses C close parentheses right parenthesis$
=> $4 R squared sin open parentheses C close parentheses left parenthesis cos open parentheses A minus B close parentheses plus cos open parentheses C close parentheses right parenthesis$
=> $4 R squared sin open parentheses C close parentheses left parenthesis cos open parentheses A minus B close parentheses plus cos open parentheses pi minus left parenthesis A plus B right parenthesis close parentheses right parenthesis$
=> $4 R squared sin open parentheses C close parentheses left parenthesis cos open parentheses A minus B close parentheses plus cos open parentheses A plus B close parentheses right parenthesis$
We know that $cos open parentheses A plus B close parentheses plus cos open parentheses A minus B close parentheses equals space 2 sin open parentheses A close parentheses sin open parentheses B close parentheses$
=> $8 R squared sin open parentheses C close parentheses sin open parentheses B close parentheses sin open parentheses A close parentheses$
Using Sine Rule
$sin open parentheses A close parentheses equals fraction numerator a over denominator 2 R end fraction comma sin open parentheses B close parentheses equals fraction numerator a over denominator 2 R end fraction comma sin open parentheses C close parentheses equals fraction numerator c over denominator 2 R end fraction$
=> $8 R squared fraction numerator a over denominator 2 R end fraction cross times fraction numerator b over denominator 2 R end fraction cross times fraction numerator c over denominator 2 R end fraction$
=> $fraction numerator a b c over denominator R end fraction$
We know that $fraction numerator a b c over denominator R end fraction equals 4 increment$
=> $4 increment$

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.