If ${\rm{\;}}\tan \,\,{\rm{\alpha }} = \frac{{\rm{m}}}{{{\rm{m}} + 1}}\,\,{\rm{and}}\,\,\tan \,\,{\rm{\beta }} = \frac{1}{{2{\rm{m}} + 1}},{\rm{\;then\;}}\,\,{\rm{\alpha }} + {\rm{\beta \;}}$ is equal to

JEE MATHEMATICS MCQ: COMPOUND ANGLES

1 Easy

1 of 1

Application +4 | -1

\mathrm{\;}\tan \,\,\mathrm{\alpha } = \frac{\mathrm{m}}{{\mathrm{m} + 1}}\,\,\mathrm{and}\,\,\tan \,\,\mathrm{\beta } = \frac{1}{{2\mathrm{m} + 1}},\mathrm{\;then\;}\,\,\mathrm{\alpha } + \mathrm{\beta \;}

is equal to

View answer and explanation

Correct option: B

\frac{\pi }{4}

Option B (

\frac{{n\pi }}{2} + \frac{\pi }{8}

) is correct because by simplifying the equation using trigonometric identities, the general solution is found to be

\frac{{n\pi }}{2} + \frac{\pi }{8}

Practice All Chapter MCQs →

\tan \left( {A + B} \right) = p

\tan \left( {A - B} \right) = q

\tan \,\,2A

\cos \,\,x\,\,\cos \,\,y\,\,\sin \,\,\left( {x - y} \right) + \cos \,\,y\,\,\cos \,\,z\,\,\sin \,\,\left( {y - z} \right)

+ \cos \,\,z\,\,\cos \,\,x\,\,\sin \,\,\left( {z - x} \right) + \sin \,\,\left( {x - y} \right)\sin \,\,\left( {y - z} \right)\,\,\sin \,\,\left( {z - x} \right)

\sin \alpha, \cos \alpha

\sqrt{1+\sin \alpha \cos \alpha}

0<\alpha<\frac{\pi}{2}

\tan \,\,A = 2\,\,\tan \,\,B + \cot \,\,B,\;\;\mathrm{then}\;\,2\,\,\tan \left( {A - B} \right)\mathrm{\;}

A,B,C

{\tan ^2}\,\,\frac{A}{2} + {\tan ^2}\,\,\frac{B}{2} + {\tan ^2}\,\,\frac{C}{2}

A > 0,\,\;B > 0

A + B = \frac{\pi }{3}

\tan A\,\,\tan B