જો cosA + cosB = cosC, sinA + sinB = sinC હોય | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

${{\rm{e}}^{{\rm{iA}}}} + {{\rm{e}}^{{\rm{iB}}}} = (\cos A + {\rm{i}}\sin {\rm{A}}) + (\cos {\rm{B}} + {\rm{i}}\sin {\rm{B}})$

$ = \cos C + i\sin C

Vedclass · Accepted Answer

$1$

Vedclass · Answer

${{m{e}}^{{m{iA}}}} + {{m{e}}^{{m{iB}}}} = (\cos A + {m{i}}\sin {m{A}}) + (\cos {m{B}} + {m{i}}\sin {m{B}})$

$ = \cos C + i\sin C = {e^{iC}}$

Also ${e^{ - iA}} + {e^{ - iB}} = {e^{ - iC}}$

$ \Rightarrow \frac{{{e^{iC}}}}{{{e^{i\left( {A + B} ight)}}}} = {e^{ - iC}} \Rightarrow {e^{2iC}} = {e^{i(A + B)}}$

$\Rightarrow \cos 2 C+i \sin 2 C$

$=\cos (A+B)+i \sin (A+B)$

$	herefore \sin (A+B)=\sin 2 C$

જો $cosA + cosB = cosC,\ sinA + sinB = sinC$ હોય તો સમીકરણ $\frac{{\sin \left( {A + B} \right)}}{{\sin 2C}}$ =

Similar Questions

જો $A = 580^o$ હોય તો નીચેનામાંથી ક્યું સાચું છે ?

$\cot {70^o} + 4\cos {70^o} = . . .$

$\frac{{\sin \theta + \sin 2\theta }}{{1 + \cos \theta + \cos 2\theta }} = $

$\cos \frac{{2\pi }}{{28}}\,\cos ec\frac{{3\pi }}{{28}}\, + \,\cos \frac{{6\pi }}{{28}}\,\cos ec\frac{{9\pi }}{{28}} + \cos \frac{{18\pi }}{{28}}\cos ec\frac{{27\pi }}{{28}}$=

$\frac{{\sec 8A - 1}}{{\sec 4A - 1}} = $