If cos A-cos B-cos C-sin A-sin B-sin Cthen the value of expression sin A-B-sin 2C is

E^iA+e^iB = cos A+cos B+i(sin A+sin B) = e^iC & e^ iA+e^ iB = e^ iC ⇒e^iC/e^iA× e^iB = e^ iC ⇒ e^2iC = e^i(A+B) ⇒cos 2C+isin2C = cos (A+B)+isin (A+B) Compa ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XI

Mathematics

Euler's Representation

If cos A+cos ...

Question

If $cos A + cos B = cos C, sin A + sin B = sin C$
then the value of expression $\frac{sin (A + B)}{sin 2 C}$ is

Open in App

Solution

$e^{i A} + e^{i B} = cos A + cos B + i (sin A + sin B) = e^{i C} & e^{- i A} + e^{- i B} = e^{- i C} \Rightarrow \frac{e^{i C}}{e^{i A} \times e^{i B}} = e^{- i C} \Rightarrow e^{2 i C} = e^{i (A + B)} \Rightarrow cos 2 C + i sin 2 C = cos (A + B) + i sin (A + B)$
Comparing the imaginary part of the equation
$sin 2 C = sin (A + B)$
$\Rightarrow \frac{sin (A + B)}{sin 2 C} = 1$

Suggest Corrections

Similar questions

Q. If

sin A + sin B + sin C = 0

and

cos A + cos B + cos C = 0

then

cos (A + B) + cos (B + C) + cos (C + A) =

Q. If

cos a + cos b + cos c = sin a + sin b + sin c = 0

then

cos (a - b) + cos (b - c) + cos (c - a) = - \frac{3}{2}

Simplify the expression:
$\frac{s i n A - s i n B}{c o s A + c o s B} + \frac{c o s A - c o s B}{s i n A + s i n B}$

Q. The value of

\frac{sin A - sin B}{cos A + cos B} + \frac{cos A - cos B}{sin A + sin B}

is....

Q. The expression

{(\frac{cos A + cos B}{sin A - sin B})}^{m} + {(\frac{sin A + sin B}{cos A - cos B})}^{m}

where

m \in N

, has the value

Join BYJU'S Learning Program

If cosA+cosB=cosC,sinA+sinB=sinC then the value of expression sin(A+B)sin2C is

eiA+eiB = cosA+cosB+i(sinA+sinB) = eiC&e−iA+e−iB = e−iC⇒eiCeiA×eiB = e−iC⇒e2iC = ei(A+B)⇒cos2C+isin2C = cos(A+B)+isin(A+B) Comparing the imaginary part of the equation sin2C = sin(A+B) ⇒sin(A+B)sin2C = 1

If $cos A + cos B = cos C, sin A + sin B = sin C$
then the value of expression $\frac{sin (A + B)}{sin 2 C}$ is