The value of $\frac{{\sin \,\,\left( {B + A} \right) + \;{\rm{cos}}\,\,\left( {B - A} \right)}}{{\sin \,\,\left( {B - A} \right) + \cos \,\,\left( {B + A} \right)}}$ is equal to

$\frac{{\cos \,\,B + \sin B}}{{\cos \,\,B - \sin \,\,B}}$

JEE MATHEMATICS MCQ: TRANSFORMATIONS

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Application +4 | -1

The value of

\frac{{\sin \,\,\left( {B + A} \right) + \;\mathrm{cos}\,\,\left( {B - A} \right)}}{{\sin \,\,\left( {B - A} \right) + \cos \,\,\left( {B + A} \right)}}

is equal to

View answer and explanation

Correct option: B

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

Option B (

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

) is correct because simplifying the given expression using trigonometric identities leads to the result

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

Practice All Chapter MCQs →

1 + \cos \,\,56^\circ + \cos \,\,58^\circ - \cos \,\,66^\circ = \lambda \cos \,\,28^\circ \,\,\cos \,\,29^\circ \,\,\sin \,\,33^\circ

\lambda =

\cos \,\,\frac{\pi }{{11}} + \cos \,\,\frac{{3\,\pi }}{{11}} + \cos \,\,\frac{{5\,\pi }}{{11}} + \cos \,\,\frac{{7\pi }}{{11}} + \cos \,\,\frac{{9\,\pi }}{{11}}

\;\cos \,\,x + \cos \,\,y + \cos \,\,\alpha = 0\;\,\mathrm{and}\,\sin x + \sin \,\,y + \sin \,\,\alpha = 0

\cot \left( {\frac{{x + y}}{2}} \right)\;

f\left( x \right) = \sin \left( {\frac{{2x + 3}}{{6\;\pi }}} \right),

0 < x,\mathrm{ }y < \pi

\cos x + \cos y - \cos (x + y) = \frac{3}{2}

\sin x + \cos y

\mathrm{\;sin}\,\,36^\circ \,\,\sin \,\,72^\circ \,\,\sin \,\,108^\circ \,\,\sin \,\,144^\circ \;