Q. 13

If A + B + C =π t

Answer :

As A+B+C = π


Then A + B = π – c



As sin π = 0 and cos (π - θ) = - cos θ



Expanding along C1 we get,




= sin B (tan A cos C) – cos C (sin B tan A)


= sin B tan A cos C – cos C sin B tan A


= 0


Hence value of .


OR


Applying R1 R1 + R2 + R3 in the given determinant, we get




Applying C1 C1 – 2C3




Expanding along the R1, we get the determinant as:


--


= (a + b + c)[(a + c – 2b)(c – a) – (b – c)(a + b – 2c)]


= (a + b + c)(ac – a2 + c2 – ac – 2bc + 2ab – ab – b2 + 2bc + ca + cb – 2c2)


= (a + b + c)(ab + ac + cb – a2 – b2 – c2)


= -(a + b + c)(a2 + b2 + c2 – ab – bc - cb)


= - (a3 + b3 + c3 – 3abc)


= 3abc – a3 – b3 – c3


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

Verify the Rolle’Mathematics - Exemplar

The value of c inMathematics - Exemplar

For the function Mathematics - Exemplar

Verify the Rolle’Mathematics - Exemplar

Verify the Rolle’Mathematics - Exemplar

Discuss theRD Sharma - Volume 1

Using Rolle’s theMathematics - Exemplar

Verify the Rolle’Mathematics - Exemplar

State True Mathematics - Exemplar

Discuss the appliMathematics - Exemplar