If $\left( {a - b} \right)\,\,\sin \,\,\left( {{\rm{\theta }} + } \right) = \left( {a + b} \right)\sin \,\,({\rm{\theta }} - \phi )\,\;{\rm{and}}\,{\rm{\;}}a\,\,\tan \,\,\frac{{\rm{\theta }}}{2}\, - \,\,b\;\tan \,\,\frac{\phi }{2} = c$, then the value of $\sin \,\,\phi $ is equal to

$\frac{{2\,ab}}{{{a^2} - \,\,{b^2} - \,\,{c^2}}}$

JEE MATHEMATICS MCQ: MULTIPLE AND SUBMULTIPLE ANGLES

1 Easy

1 of 1

Analyzing +4 | -1

\left( {a - b} \right)\,\,\sin \,\,\left( {\mathrm{\theta } + } \right) = \left( {a + b} \right)\sin \,\,(\mathrm{\theta } - \phi )\,\;\mathrm{and}\,\mathrm{\;}a\,\,\tan \,\,\frac{\mathrm{\theta }}{2}\, - \,\,b\;\tan \,\,\frac{\phi }{2} = c

, then the value of

\sin \,\,\phi

is equal to

View answer and explanation

Correct option: B

\frac{{2\,bc}}{{{a^2} - \,\,{b^2} - \,\,{c^2}}}

Option C (

\frac{{2\,bc}}{{{{a^2} - \,{b^2} + \,{c^2}}}}

) is correct because after simplification and substitution using the given equations, it leads to the correct expression for sin(

\phi